The dispersive power of material of a lens of focal length 20 cm is 0 . 08 . Find the longitudinal chromatic aberration of the lens?

Chromatic aberration is defined as the failure of an optical lens to focus different wavelengths of light to the same point. It is caused by dispersion. Dispersion is a phenomenon in which the phase velocity of a wave depends on its frequency. Rainbow is a beautiful result of dispersion. Due to dispersion, the refractive index for every wavelength is different. Since, white light consists of seven colours viz. violet, indigo, blue, yellow, green, orange, and red; which are of different wavelengths. The refractive index for these colours is also different. That is why they converge at different points and cause longitudinal chromatic aberration. The refractive index of any medium or material is inversely proportional to the wavelength of light passing through it. μ ∝ 1 λ Mathematically, we can define longitudinal chromatic as a product of the dispersion power and the mean focal length of the lens. i.e., c = ω f let put in the values 0 . 08 = ω 20 ω = 1 . 6 cm .

The dispersive powers of the material of the two lenses are in the ratio of 4 3 . If the focal length of this achromatic combination is 60 cm , find the focal length of the lenses.

For an achromatic combination of lenses, f 1 f 2 = - ω 1 ω 2 . . . i here: ω 1 ω 2 = 4 3 . . . ii From the equation i and ii So, f 1 f 2 = - 4 3 or f 1 f 2 = - 4 3 f 2 . Now the combined focal length of the lens is given by 1 F = 1 f 1 + 1 f 2 1 60 = - 3 4 f 2 + 1 f 2 ∵ F = 60 cm 1 60 = - 3 + 4 4 f 2 4 f 2 = 60 ∴ f 2 = 15 cm and f 1 = - 4 3 f 2 f 1 = - 4 3 × 15 f 1 = - 20 cm . Hence, the focal length of component lenses is + 15 cm and - 20 cm .

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Beta Question Bank for Medical: Physics>Chapter 30 - Ray Optics>BEGINNER'S BOX - 7>Q 2

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An achromatic doublet of focal length 90 cm si to be made of two lens. The material of one of the lenses has 1.5 times the dispersive power of the other. The doublet is converting type. Find the focal length of each lens.

Important Questions on Ray Optics

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Beta Question Bank for Medical: Physics>Chapter 30 - Ray Optics>BEGINNER'S BOX - 7>Q 3

The dispersive power of material of a lens of focal length

20 cm

is

f_{2} = - 45 cm

. Find the longitudinal chromatic aberration of the lens?

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Beta Question Bank for Medical: Physics>Chapter 30 - Ray Optics>BEGINNER'S BOX - 7>Q 4

The dispersive powers of the material of the two lenses are in the ratio of

\frac{4}{3}

. If the focal length of this achromatic combination is

60 cm

, find the focal length of the lenses.

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Beta Question Bank for Medical: Physics>Chapter 30 - Ray Optics>BEGINNER'S BOX - 7>Q 5

What is the axial chromatic aberration in case of a lens which focusses violet ray 20.1 cm and red ray 20.3 cm away from it.

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Beta Question Bank for Medical: Physics>Chapter 30 - Ray Optics>BEGINNER'S BOX - 8>Q 1

The angle of incidence is

45 °

in the condition of minimum deviation for a prism of refracting angle

60 °

. Find the angle of deviation.

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Beta Question Bank for Medical: Physics>Chapter 30 - Ray Optics>BEGINNER'S BOX - 8>Q 2

A light ray is an incident normally on the surface $A B$ of a prism of refracting angle $60 °$ . If the light ray does not emerge from $A C$ , then find the refractive index of the prism.

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