Question

The variation of refractive index of a crown glass thin prism with wavelength of the incident light is shown. Which of the following graphs is the correct one, if $D_m$ is the angle of minimum deviation?

• A.

  

• B.

  

• C.

  

• D.

  

Answer 1

The correct option is B

The explanation for the correct answer:-

Option (B)

1. Since $D_m=(\mu -1)A$ for a thin prism,
   Where $D_m=Angleofminimumdeviation$ and $\mu$ is the refractive index and $A$ is the angle of the prism.
2. Hence the more the refractive index, and more will be the deviation.
3. The angle of minimum deviation varies with the refractive index.
4. If the value of the refractive index increases then the angle of minimum deviation also increases.
5. The formula of the refractive index of the material is $\mu =\frac{c}{v}$ and the formula of the wavelength,$\lambda =\frac{c}{\mu f}$.
   Where $c$ is the velocity of light in vacuum, $\lambda$ is the wavelength, the refractive index of a material is $\mu$, $f$ is the frequency and $v$ is the velocity of light in a material,
   
6. Therefore the correct answer is B

The explanation for the incorrect answer:-

Option (A)

1. In comparison to crown glass, flint glass will bend the ray more, leading to a higher angle of departure
2. Option A is incorrect

Option (C)

1. To create dispersion without deviation, two glass prisms—a flint prism and a crown prism—are joined.
2. Since the flint glass has a higher refractive index than crown glass, it will bend the emerging ray more, producing a larger deviation angle.
3. Option (C) is incorrect

Option (D)

1. The flint glass prism distorts the light ray more.
2. Option D is incorrect.

Therefore, option (B) is the correct answer.