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.

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Two lenses, one concave and the other convex of same power are placed such that their principal axes coincide. If the separation between the lenses is $x$ , then

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Important Questions on Ray Optics and Optical Instruments

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Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

A thin convex lens of focal length

f

is put on a plane mirror as shown in the figure. When an object is kept at a distance

a

from the lens-mirror combination, its image is formed at a distance

\frac{a}{3}

in front of the combination. The value of

a

is:

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Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

Two convex lenses $A$ & $B$ placed in contact form the image of a distant object at $P .$ If the lens $B$ is moved to the right a little, the image will

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Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

Two thin biconvex lenses have focal lengths

f_{1}

and

f_{2}

. A third thin biconcave lens has focal length of

f_{3} .

If the two biconvex lenses are in contact, the total power of the lenses is

P_{1}

. If the first convex lens is in contact with the third lens, the total power is

P_{2}

. If the second lens is in contact with the third lens, the total power is

P_{3}

then

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Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

A person cannot see objects clearly beyond

2.0 m

. The power of lens required to correct his vision will be

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Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

A thin convex lens

L

(refractive index

= 1.5

) is placed on a plane mirror

M

. When a pin is placed at

A

, such that

O A = 18 c m,

its real inverted image is formed at

A

itself, as shown in figure. When liquid of refractive index

μ_{l}

is put between the lens and the mirror, the pin has to be moved to

A^{'},

such that

O A^{'} = 27 c m,

to get its inverted real image at

A'

itself. The value of

μ_{l}

will be

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Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

Curved surfaces of a plano-convex lens of refractive index $μ_{1}$ and a plano-concave lens of refractive index $μ_{2}$ have equal radius of curvature as shown in figure. Find the ratio of radius of curvature to the focal length of the combined lenses

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EASY

Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

Two thin lenses of focal length

f_{1}

and

f_{2}

are in contact and coaxial. The power of the combination is

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Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

When two thin lenses are kept in contact, prove that their combined or effective focal length F is given by:

\frac{1}{F} = \frac{1}{F_{1}} + \frac{1}{F_{2}}

where the terms have their usual meaning.

EASY

Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

Two thin lenses are in contact and the focal length of the combination is

80 cm

. If the focal length of one lens is

20 cm

, then the power of the other lens will be

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Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

A convex lens is in contact with a concave lens. The magnitude of the ratio of their focal length is

\frac{5}{3} .

If their equivalent focal length is

45 cm,

the individual focal lengths of concave and convex lens are respectively.

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Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

Two lenses of power

8 D

and

- 4 D

are combined. Calculate the focal length of the combined lens.

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Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

Two identical glass

(μ_{g} = \frac{3}{2})

equiconvex lenses of focal length,

f

are kept in contact. The space between the two lenses is filled with water

(μ_{w} = \frac{4}{3})

. The focal length of the combination is

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Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

Deduce the equivalent focal length of two convex lenses of focal lengths $f_{1} and f_{2}$ , when placed in contact.

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Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

Two equiconvex lenses, each of refractive index

1.5

and focal length

' f'

are kept in contact with each other, and the space in between the lenses is filled with a liquid of refractive index

1.75 .

The focal length of the combination is

HARD

Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

Find an expression for combined focal length of two thin coaxial convex lenses placed in contact.

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Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

Show that the effective power of two thin lenses in contact is the sum of the power of each lens.

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Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

For two thin lenses kept in contact with each other, show that:

$\frac{1}{F} = \frac{1}{f_{1}} + \frac{1}{f_{2}}$

where the terms have their usual meaning.

HARD

Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

Two identical equiconvex lenses, each of focal length $f$ are placed side by side in contact with each other with a layer of water in between them as shown in the figure. If refractive index of the material of the lenses is greater than that of water, how the combined focal length $F$ is related to $f ?$

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Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

Two similar thin equi-convex lenses of focal length

f

each are kept coaxially in contact with each other, such that the focal length of the combination is

F_{1} .

When the space between the two lenses is filled with glycerin (which has the same refractive index (

μ = 1.5

) as that of glass), then the equivalent focal length is

F_{2} .

The ratio

F_{1} : F_{2}

will be

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Physics>Optics>Ray Optics and Optical Instruments>Refraction at Spherical Surfaces and by Lenses

Two thin lenses have a combined power of

+ 9 D .

When they are separated by a distance of

20 cm,

their equivalent power becomes

+ \frac{27}{5} D,

then their individual powers are

Two lenses, one concave and the other convex of same power are placed such that their principal axes coincide. If the separation between the lenses is x, then

Important Questions on Ray Optics and Optical Instruments

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Two lenses, one concave and the other convex of same power are placed such that their principal axes coincide. If the separation between the lenses is $x$ , then