Refraction Through Lens Class 10 ICSE — Selina Chapter 5

Refraction through lens class 10 icse is the chapter where ray diagrams meet calculation. It explains how a convex lens converges light and a concave lens diverges it, how to draw the three principal rays, and how every numerical is solved with one formula. The chapter also covers magnification, power of a lens, the magnifying glass, and two lab methods for measuring focal length.

Download Refraction Through a Lens Class 10 ICSE Physics Chapter 5 PDF

Download the Refraction Through a Lens Class 10 ICSE Physics chapter PDF from the Selina Concise textbook to revise offline or print for practice. It is the full chapter as printed in the book — 29 pages, 15 sections, 67 questions.

What is inside Chapter 5

29 pages · 15 sections · 2 worked examples · 67 exercise questions

• MULTIPLE CHOICE TYPE: 2 questions
• EXERCISE-5(B): 29 questions
• MULTIPLE CHOICE TYPE: 3 questions
• EXERCISE-5(C): 9 questions
• MULTIPLE CHOICE TYPE: 15 questions
• EXERCISE-5(D): 7 questions
• MULTIPLE CHOICE TYPE: 2 questions

5.1 LENS

A lens is a transparent refracting medium bounded by two spherical surfaces, or by one spherical surface and one plane surface. A plane surface counts as a spherical surface of infinite radius of curvature, so the same definition covers it.

Lenses come in two kinds. A convex (converging) lens is thick in the middle and thin at the edge, and it bends parallel light toward a point. A concave (diverging) lens is thin in the middle and thick at the edge, and it spreads parallel light away from the axis.

Each kind has three shapes:

• Convex: biconvex, plano-convex, concavo-convex.
• Concave: biconcave, plano-concave, convexo-concave.

Students often confuse the two mixed shapes. A concavo-convex lens is thicker in the middle, so it converges light. A convexo-concave lens is thinner in the middle, so it diverges light. The shape decides the action, not the order of the names.

5.2 ACTION OF A LENS AS A SET OF PRISMS

The prism model explains lens action. Think of a lens as a set of prisms: a rectangular glass slab in the centre, with one prism on either side. A ray of light always bends toward the base of a prism on refraction.

In a convex lens, the upper prism has its base downward, so it bends the upper ray down. The lower prism has its base upward, so it bends the lower ray up. The central slab passes a normally incident ray undeviated. The rays converge, which is why the lens is converging.

This is the same bend-toward-the-base rule you met in the chapter on refraction of light at plane surfaces.

A concave lens reverses the prism bases. The upper prism bends its ray up, and the lower prism bends its ray down. The rays spread apart as if they came from a single point F on the incident side. That is the diverging action.

5.3 TECHNICAL TERMS RELATED TO A LENS

Each surface of a lens is part of a sphere. The centre of that sphere is the centre of curvature of that surface, so a lens has two centres of curvature, C_1 and C_2. The radius of that sphere is the radius of curvature. For a thin lens, the radius equals the distance from the centre of curvature to the optical centre, so PC_1 = OC_1.

An equi-convex or equi-concave lens has equal radii on both surfaces, OC_1 = OC_2.

The principal axis is the line joining the two centres of curvature, C_1C_2. The optical centre O lies on this axis. A ray directed at O passes through undeviated, because the central part behaves like a parallel-sided slab and the lateral shift in a thin lens is too small to matter.

A lens has two principal foci. The first focus F_1 is the point from which rays become parallel to the axis after refraction. The second focus F_2 is where rays incident parallel to the axis converge (convex lens) or appear to diverge from (concave lens). Focal planes pass through the foci, normal to the principal axis.

The focal length is the distance from O to the focus, so the first focal length is OF_1 and the second is OF_2. When the medium is the same on both sides, f_1 = f_2. A convex lens has a real focus; a concave lens has a virtual focus.

Two factors set the focal length. The first is the refractive index of the lens material relative to its surroundings, so a lens in water has a larger focal length than in air. The second is the radii of curvature, so a thick lens has a smaller focal length than a thin lens of the same material.

If part of a lens is covered, the focal length does not change. Only the light entering the lens decreases, so the image turns dimmer. The position, size and nature of the image stay the same.

An oblique parallel beam does not meet at F_2. It converges at a point in the second focal plane, where the ray through the optical centre meets that plane.

5.5 PRINCIPAL (OR CONSTRUCTION) RAYS FOR RAY DIAGRAMS

Ray diagrams use rays whose path after refraction is known. Three principal rays serve every construction:

• A ray through the optical centre O passes undeviated.
• A ray parallel to the principal axis passes through F_2 (convex) or appears to come from F_2 (concave) after refraction.
• A ray through F_1 (convex), or directed at F_1 (concave), emerges parallel to the axis.

From any point on the object, choose two of these rays. Where the refracted rays meet, or appear to meet, is the image of that point. Doing this for each point builds the full image.

Images are of two kinds. A real image forms where refracted rays actually meet, so a screen placed there shows it. A virtual image forms where rays only appear to meet when produced backward; a screen shows nothing there. The eye still sees it, because the eye lens converges the diverging rays onto the retina.

5.6 CONSTRUCTION OF RAY DIAGRAM FOR A LENS

The drawing method is the same for both lenses.

1. Draw the principal axis PQ, choose the optical centre O, and mark the lens as a vertical line through O.
2. Mark F_1 and F_2 at equal distances on either side of O, since air is on both sides: OF_1 = OF_2.
3. Draw the object AB on the axis at the given height and position.
4. From the top point A, draw a ray AO through the optical centre, undeviated.
5. From A, draw a ray AD parallel to the axis; after refraction it passes through F_2. The alternative is a ray through F_1, which emerges parallel to the axis.
6. The point A’ where the refracted rays meet is the image of A. Drop a perpendicular A’B’ to the axis to complete the image.

For a concave lens the foci swap sides: F_1 lies to the right of O and F_2 to the left. The refracted rays never actually meet; produced backward they meet at A’, giving a virtual image.

5.7 CHARACTERISTICS AND LOCATION OF IMAGES FOR A CONVEX LENS

A convex lens of focal length f forms a different image for each object position. The six positions below are the ones board questions repeat in this Class 10 ICSE chapter.

The trend is easy to follow. As the object moves from infinity toward the lens, the image moves away from F_2, grows steadily, and stays real and inverted until the object reaches F_1. Once the object crosses inside the focus, the image becomes virtual, erect and magnified, on the same side behind the object.

An object far off gives a real, inverted, highly diminished image at the focus. Moving the lens toward the object produces the same sequence as moving the object toward the lens.

5.8 CHARACTERISTICS AND LOCATION OF IMAGES FOR A CONCAVE LENS

A concave lens has only two object positions to study. When the object is at infinity, parallel rays appear to diverge from F_2 after refraction. The image is virtual, erect, highly diminished, and sits at F_2 on the side of the object. A concave lens used this way is the objective of a Galilean telescope.

When the object is at any finite distance, the ray through the optical centre passes undeviated, and the ray parallel to the axis appears to come from F_2. Produced backward, the rays meet to form a virtual, erect, diminished image between the lens and the focus, on the object side. Spectacles for myopia work on this case.

The standing result: for every object position, a concave lens gives a virtual, upright, diminished image on the side of the object, between the focus and the lens. One special case is worth noting. When the object is at a distance equal to the focal length, the image lies exactly midway between the optical centre and the second focus.

5.10 SIGN CONVENTION OF MEASUREMENT OF DISTANCES

The Cartesian sign convention is the numbering rule for every lens numerical. Its five rules are:

• The optical centre O is the origin.
• The object is placed on the left of the lens.
• All distances are measured along the principal axis from O.
• Distances in the direction of the incident ray are positive; distances opposite to it are negative.
• Heights above the principal axis are positive; heights below it are negative.

Applied to lenses, the convention gives three practical signs:

• u is always negative, because the object lies opposite to the incident ray’s direction.
• f is positive for a convex lens and negative for a concave lens.
• v is positive for a real image behind the lens, and negative for a virtual image in front of it.

5.11 LENS FORMULA 1/v – 1/u = 1/f

The lens formula links object distance u, image distance v and focal length f:

\frac{1}{v} - \frac{1}{u} = \frac{1}{f}

The same formula holds for both convex and concave lenses. The derivation uses similar triangles in the ray diagram, then applies the sign convention. For a convex lens, u is negative while f and a real-image v are positive. For a concave lens, u, v and f are all negative, and the numerical value of u is always greater than v.

Both cases simplify to the same expression.

Worked example with fresh numbers: a 3 cm tall object stands 30 cm in front of a convex lens of focal length 10 cm. Substitute u = -30\ \text{cm} and f = +10\ \text{cm}:

\frac{1}{v} = \frac{1}{f} + \frac{1}{u} = \frac{1}{10} + \frac{1}{-30} = \frac{2}{30}

So v = +15\ \text{cm}. The image is real, 15 cm behind the lens. Magnification m = v/u = 15/(-30) = -0.5, so the image is 1.5 cm tall, inverted and diminished.

Common mistakes to avoid in this ICSE chapter:

• Substituting u as positive. The object is on the left, so u is always negative.
• Using 1/u + 1/v = 1/f. The correct form under the Cartesian sign convention is 1/v - 1/u = 1/f.
• Marking v positive for a virtual image. A virtual image in front of the lens takes a negative v.

5.12 LINEAR MAGNIFICATION

Linear magnification compares the length of the image I with the length of the object O:

m = \frac{I}{O} = \frac{v}{u}

The sign of m tells the nature of the image. A negative m means a real, inverted image. A positive m means a virtual, erect image. A convex lens can give either sign; a concave lens always gives a positive m.

The numerical value of m tells the size. A value greater than 1 means magnified, equal to 1 means same size, and less than 1 means diminished. A concave lens always gives m less than 1. A convex lens can give all three, depending on the object’s position.

In the worked example above, m = -0.5. The negative sign says real and inverted. The value 0.5 says the image is half the object’s height.

5.13 POWER OF A LENS

Power measures how strongly a lens deviates light. A lens that bends rays more has more power. A thick lens deviates more and has a short focal length, so power is the reciprocal of focal length:

P = \frac{1}{f}

with f in metres. The unit is the dioptre (D). A lens of power 1 D has a focal length of exactly 1 m, or 100 cm.

The sign of power comes from the direction of deviation. A convex lens bends rays toward its centre, so its power is positive. A concave lens bends rays away from its centre, so its power is negative. A convex lens of focal length 20 cm has power +5.0 D; a concave lens of the same focal length has power -5.0 D.

As a check: a concave lens of focal length 25 cm gives f = -0.25\ \text{m}, so P = -4\ \text{D}.

When two thin lenses are placed in contact, their powers add algebraically. A convex lens of +2.0 D in contact with a concave lens of -2.0 D gives zero power, and the pair behaves like a glass plate.

5.14 MAGNIFYING GLASS OR SIMPLE MICROSCOPE

The magnifying glass, or simple microscope, is a convex lens of short focal length. Its principle rests on the least distance of distinct vision, D = 25 cm for a normal eye. An object closer than D cannot be seen clearly, so the lens is placed so the object lies within its focal length. The lens then forms an erect, virtual, magnified image at the distance D.

Magnifying power is given by:

m = 1 + \frac{D}{f}

A shorter focal length raises the magnifying power. For a lens of f = 10\ \text{cm}, m = 1 + 25/10 = 3.5, so the object appears three and a half times larger. The power cannot be increased without limit, because the focal length would become impractically short.

The simple microscope works as a reading lens. Watch makers use it for small parts and screws. Travelling microscopes and spectrometers carry one above the vernier scale so the scale can be read accurately.

5.15 APPLICATION OF LENSES

• The objective lens of a telescope, camera or slide projector is a convex lens forming a real, inverted image.
• The eye lens is a convex lens; it forms an inverted image on the retina.
• Spectacles: a convex lens corrects hypermetropia for near objects, and a concave lens corrects myopia for distant objects. A bifocal lens combines both, with the concave part above for distance and the convex part below for near work.
• A magnifying glass is a short-focal-length convex lens in a frame with a handle.
• A collimator of a spectroscope uses a convex lens to produce a parallel beam.
• A Galilean telescope uses a concave objective lens to give an erect final image.
• A single convex lens forms a coloured, blurred image because of chromatic aberration. Adding a concave lens corrects it — the same defect that the spectrum chapter takes up.

5.16 EXPERIMENTAL DETERMINATION OF FOCAL LENGTH OF A CONVEX LENS

Distant object method: a distant tree or pole sends nearly parallel rays to the lens, and these converge in the focal plane. Hold a metre rule horizontally against a white wall, with the zero end at the wall. Move the lens along the rule until a sharp image forms on the wall. The lens-to-wall distance read on the rule is the approximate focal length.

Plane mirror method: place the convex lens on a plane mirror. Clamp a pin horizontally so its tip sits vertically above the optical centre. Adjust the pin height until its inverted image shows no parallax — move the eye sideways, and the pin tip and image tip must shift together.

Why the rays return: rays from the pin become parallel after passing through the lens and strike the mirror normally, so they reflect straight back along the same path. The lens then refocuses them at the pin, forming a real, inverted image of the same size.

Measure x, the pin-to-lens distance, and y, the pin-to-mirror distance, and take the average:

f = \frac{x + y}{2}

Repeat the measurement for three settings and average the readings. On an optical bench, note the pin position x_1 and the lens position x_2; then f = x_2 - x_1. The mirror may be moved without changing the result, as long as the rays still fall normally on it.

5.17 TO DIFFERENTIATE BETWEEN A CONVEX AND A CONCAVE LENS

Three quick tests separate the two lenses without any apparatus:

• By touch: thick in the middle and thin at the edge means convex; thin in the middle and thick at the edge means concave.
• Near a printed page: magnified letters mean convex; diminished letters mean concave.
• At a distant object: an inverted image means convex; an upright image means concave.

The tests use properties already established. A convex lens magnifies inside the focus and inverts distant objects. A concave lens always gives an upright, diminished image.

What to practise from Refraction Through Lens Class 10 ICSE

The question blocks follow the chapter’s order. Exercise 5(B) works through ray diagrams, the principal rays, and the image characteristics of both lenses. Exercises 5(C) and 5(D) run the numericals: sign convention, lens formula, magnification, power, and the focal length experiments.

• Exercise 5(B) — 29 questions.
• Exercise 5(C) — 9 questions.
• Exercise 5(D) — 7 questions.
• Multiple choice type sets — 22 questions in four sets (2, 3, 15 and 2).

All of these sit inside the Class 10 ICSE Physics collection on this site. For the official scope of the Class 10 Physics syllabus, see the CISCE website.

Refraction Through Lens Class 10 ICSE frequently asked questions

What is the lens formula for refraction through lens class 10 icse?

The lens formula is \frac{1}{v} - \frac{1}{u} = \frac{1}{f}, where u is the object distance, v the image distance and f the focal length. It works for both convex and concave lenses, as long as every distance carries its proper sign.

When does a convex lens form a virtual, erect and magnified image?

When the object lies between the optical centre and the first focus F_1, that is u \lt f. The image then forms on the same side, behind the object, and the application is the magnifying glass.

Why is the focal length of a concave lens taken as negative?

In the Cartesian sign convention, distances opposite to the direction of the incident ray are negative. A concave lens has a virtual focus on the incident side, so its f is negative. Its images are virtual and in front of the lens, so v is negative too.

How is the focal length of a convex lens found using a plane mirror?

Place the lens on the plane mirror and adjust a pin until its inverted image shows no parallax. Rays return along the same path because they strike the mirror normally. Measure x, the pin-to-lens distance, and y, the pin-to-mirror distance; then f = (x + y)/2.

What is the power of a lens and why is its unit the dioptre?

Power is the reciprocal of the focal length measured in metres, P = 1/f. The unit is the dioptre (D) because a lens of focal length exactly 1 m has power exactly 1 D. Convex lenses have positive power and concave lenses negative power.

The syllabus this chapter follows is set by the CISCE board.

Reference: ICSE Class 10 Physics textbook material, chapter 5: Refraction Through a Lens — CISCE-aligned.

More from this book

• Chapter 1: Force
• Chapter 2: Work Energy and Power
• Chapter 3: Machines
• Chapter 4: Refraction of Light At Plane Surfaces
• Chapter 6: Spectrum
• Chapter 7: Sound
• Chapter 8: Current Electricity
• Chapter 9: Household Circuits
• Chapter 10: Electro Magnetism
• Chapter 11: Calorimetry
• Chapter 12: Radioactivity