Question

Assertion: When a white light is passed through a lens, violet light is more diffracted than red light.
Reason: Focal length for red light is greater than violet.
A) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B) Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C) Assertion is correct but Reason is incorrect.
D) Both Assertion and Reason are incorrect.

Answer 1

Hint: Think about the dependency of wavelength, focal length and refractive index with each other. Also compare the wavelength of red and violet light. In the spectrum of light, red with maximum wavelength and violet light has the minimum wavelength.

Complete step by step solution:
We know refractive index is related with wavelength by
$\mu \propto \dfrac{1}{\lambda }$
Since the wavelength of red is greater than that of violet, refractive index of violet light is more than that of red light.
Now, the refractive index and focal length are related by
$\dfrac{1}{f} = \left( {{\mu _{rel}} - 1} \right)\left( {\dfrac{1}{{{R_1}}} - \dfrac{1}{{{R_2}}}} \right)$
Thus the focal length increases when the refractive index decreases.
Deviation is the angle by which a refracted ray deviates from its original path before refraction. More deviation means that a ray is more refracted.
Also, deviation is related to refractive index as
$\delta = A\left( {\mu - 1} \right)$
Thus deviation is more for a greater refractive index.
Finally from the above equations we can tell that,
${\mu _V} > {\mu _R}$
${f_R} > {f_V}$
${\delta _V} > {\delta _R}$
Since, violet light has greater refractive index thus when a white light is passed through a lens, violet light is more diffracted than red light.
Also from the above deduced relations we get that,
Focal length for red light is greater than violet.
Hence, both Assertion and Reason are correct and Reason is the correct explanation for Assertion.

Hence, Option (A) is correct.

Note: Write the correct relation between refractive index, focal length and deviation of violet light and red light. Also make sure that the reason is apt for the given assertion.