The focal length of a convex lens made of flint glass is $15 c m$ . To remove its chromatic aberration, it is placed in contact with a concave lens made of crown glass. Find the focal length of the concave lens. The ratio of dispersive powers of flint glass to crown glass is $1.5$ .

Question

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Answer 1

Given: The focal length of a convex lens made of flint glass is 15cm. To remove its chromatic aberration, it is placed in contact with a concave lens made of crown glass. The ratio of dispersive powers of flint glass to crown glass is 1.5.
To find the focal length of the concave lens
Solution:
Let focal length of the convex lens be $f_{1}$ and focal length of the concave lens be $f_{2}$ and ratio of dispersice power of the flint glass is $$\dfrac {\omega_2}{\omega_1}=1.5$$
For achromatic combination,

$\frac{f _{1}}{f _{2}} = - \frac{ω _{2}}{ω _{1}} ⟹ \frac{1 5}{f _{2}} = - 1.5 ⟹ f_{2} = - 10 c m$
Hence the focal length of the concave lens is -10cm

Answer 2

Given: The focal length of a convex lens made of flint glass is 15cm. To remove its chromatic aberration, it is placed in contact with a concave lens made of crown glass. The ratio of dispersive powers of flint glass to crown glass is 1.5.

To find the focal length of the concave lens

Solution:

Let focal length of the convex lens be

f_{1}

and focal length of the concave lens be

f_{2}

and ratio of dispersice power of the flint glass is $$\dfrac {\omega_2}{\omega_1}=1.5$$

For achromatic combination,

\frac{f _{1}}{f _{2}} = - \frac{ω _{2}}{ω _{1}} ⟹ \frac{1 5}{f _{2}} = - 1.5 ⟹ f_{2} = - 10 c m

Hence the focal length of the concave lens is -10cm

The focal length of a convex lens made of flint glass is $15 c m$ . To remove its chromatic aberration, it is placed in contact with a concave lens made of crown glass. Find the focal length of the concave lens. The ratio of dispersive powers of flint glass to crown glass is $1.5$ .

$- 10 c m$

$+ 10 c m$

$- 20 c m$

$+ 20 c m$

In chromatic aberration of a convex lens, :

Chromatic aberration(distance between the focal lengths for extreme wavelengths) of a convex lens can be reduced by(Assume lenses are kept in vacuum)

The refractive indices of the material of a lens for violet, yellow and red colours of light are respectively $1.66, 1.64$ and $1.62$ . The mean focal length of the lens is $10 c m$ . Determine the chromatics aberration of the lens between the violet and the red colors.

For which of the two lenses $L_{1}$ and $L_{2}$ the chromatic aberration will be more if the dispersive power of the material of $L_{1}$ is less than that of $L_{2}$ :

Why is the focal point for any convex lens a little inexact with ordinary white light?

Revise with Concepts

Chromatic Aberration

The focal length of a convex lens made of flint glass is 15cm. To remove its chromatic aberration, it is placed in contact with a concave lens made of crown glass. Find the focal length of the concave lens. The ratio of dispersive powers of flint glass to crown glass is 1.5.

−10cm

+10cm

−20cm

+20cm

In chromatic aberration of a convex lens, :

Chromatic aberration(distance between the focal lengths for extreme wavelengths) of a convex lens can be reduced by(Assume lenses are kept in vacuum)

The refractive indices of the material of a lens for violet, yellow and red colours of light are respectively 1.66,1.64 and 1.62. The mean focal length of the lens is 10cm. Determine the chromatics aberration of the lens between the violet and the red colors.

For which of the two lenses L1​ and L2​ the chromatic aberration will be more if the dispersive power of the material of L1​ is less than that of L2​:

Why is the focal point for any convex lens a little inexact with ordinary white light?

Revise with Concepts

Chromatic Aberration

The focal length of a convex lens made of flint glass is $15 c m$ . To remove its chromatic aberration, it is placed in contact with a concave lens made of crown glass. Find the focal length of the concave lens. The ratio of dispersive powers of flint glass to crown glass is $1.5$ .

$- 10 c m$

$+ 10 c m$

$- 20 c m$

$+ 20 c m$

The refractive indices of the material of a lens for violet, yellow and red colours of light are respectively $1.66, 1.64$ and $1.62$ . The mean focal length of the lens is $10 c m$ . Determine the chromatics aberration of the lens between the violet and the red colors.

For which of the two lenses $L_{1}$ and $L_{2}$ the chromatic aberration will be more if the dispersive power of the material of $L_{1}$ is less than that of $L_{2}$ :