For two thin lenses kept in contact with each other, show that: 1 F = 1 f 1 + 1 f 2 where the terms have their usual meaning.

Let two lenses A and B kept in contact and the object is kept at the point O beyond the focus of the first lens A. The first lens produces an image at I 1 . Since image I 1 is real, it serves as a virtual object for the second lens B, producing the final image at I. Since the lenses are thin, we assume the optical centres of the lenses to be coincident. Let this central point be denoted by P. For the image formed by the first lens A, we get: 1 f 1 = 1 v 1 - 1 u .....(i) For the image formed by the second lens B, we get 1 f 1 = 1 v - 1 v 1 .....(ii) On adding (i) and(ii) we get: 1 f 1 + 1 f 2 = 1 v - 1 u .....(iii) If the two lens system is considered as a single lens of focal length F , we can write: 1 F = 1 v - 1 u ......(iv) From(iii) and(iv) we get: 1 F = 1 f 1 + 1 f 2 ....(v) v is the required expression.

When two thin lenses are kept in contact, prove that their combined or effective focal length F is given by: 1 F = 1 F 1 + 1 F 2 where the terms have their usual meaning.

Let a point object O is placed on the principal axis By lens formula for image formation by lens L 1 1 v ' - 1 u = 1 f 1 -------------------(1) I' serves as a virtual object for the second lens L 2 which forms a final image I at a distance ' v ' . Then for L 2 1 v - 1 v ' = 1 f 2 -----------------(2) Adding equation (1) and (2) 1 v - 1 u = 1 f 1 + 1 f 2 ----------- (3) If we replace these two lenses by a single lens such that if an object is kept at u image is formed at v then its focal length f is given by 1 v - 1 u = 1 f ------------- (4) From equation (3) and (4) we get 1 f = 1 f 1 + 1 f 2

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A convex lens is cut into two parts in different ways that are arranged in four manners, as shown. Which arrangement will give maximum optical power?

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Important Questions on Refraction of Light at Spherical Surfaces : Lenses

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Refraction of Light at Spherical Surfaces : Lenses>Exercise>Q 4

What will happen when the following rays are incident on a convex lens of focal length $20 cm;$ a diverging beam of rays coming from a point $5 cm$ away from the lens.

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Refraction of Light at Spherical Surfaces : Lenses>Exercise>Q 5

The lower half of a convex lens is made of material of refractive index

n_{1}

and the upper half has refractive index

n_{2}

. If a point source of light is placed on the principal axis which kind of image is formed by it?

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Refraction of Light at Spherical Surfaces : Lenses>Exercise>Q 6

A convex lens is placed over a plane mirror. If a point source of light is placed at the focus of the lens where will the image be formed? Draw the ray diagram.

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Refraction of Light at Spherical Surfaces : Lenses>Exercise>Q 7

A convex lens is placed on a plane mirror. Draw the ray diagram when a point source of light is placed at the focus of the lens.

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Refraction of Light at Spherical Surfaces : Lenses>Exercise>Q 8

The refractive index of material of a Plano-convex lens, if the radius of curvature of the plane surface

(R_{1})

is infinite while the radius of curvature of convex surface

(R_{2})

20 c m

and focal length of the lens is

30 c m

, will be:

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Refraction of Light at Spherical Surfaces : Lenses>Exercise>Q 9

An equiconvex lens of r.i.

1.5

and focal length

10 cm

is so placed that the upper half of the lens is in air and lower half immersed in water of r.i.

4 / 3

. An object is placed in air along the vertical axis at a distance of

50 cm

from the lens. At what distance from the lens will the image be focussed?

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Refraction of Light at Spherical Surfaces : Lenses>Exercise>Q 10

A biconvex lens made of glass (refractive index

1.5

) has two spherical surfaces having radii

20 c m

and

30 c m

. Calculate its focal length.

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 3 - Refraction of Light at Spherical Surfaces : Lenses>Exercise>Q 11

A thin convergent glass lens μ=1.5 has a power of $+ 5 D$ . When this lens is immersed in a liquid of refractive index $n$ it acts as a diverging lens of focal length $100 cm$ . The value of $n$ must be :

A convex lens is cut into two parts in different ways that are arranged in four manners, as shown. Which arrangement will give maximum optical power?

Important Questions on Refraction of Light at Spherical Surfaces : Lenses

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