Physics - Geometrical Optics Question with Solution | TestHub
A light ray is incident on the surface of a sphere of refractive index at an angle of incidence . The ray partially refracts into the sphere with angle of refraction and then partly reflects from the back surface. The reflected ray then emerges out of the sphere after a partial refraction. The total angle of deviation of the emergent ray with respect to the incident ray is . Match the quantities mentioned in List-I with their values in List-II and choose the correct option.
List - I | List - II |
|---|---|
(I) If $n = 2$ and $\alpha = 180^\circ$, then all the possible values of $\theta_0$ will be | (P) |
(II) If $n = \sqrt{3}$ and $\alpha = 180^\circ$, then all the possible values of $\theta_0$ will be | (Q) |
(III) If $n = \sqrt{3}$ and $\alpha = 180^\circ$, then all the possible values of $\phi_0$ will be | (R) |
(IV) If $n = 2$ and $\theta_0 = 45^\circ$, then all the possible values of $\alpha$ will be | (S) |
| (T) |
Options:
Answer:
Solution:
Each refraction deviates the ray by and the internal reflection by , so with .
For : . With : , only (I → T).
With : , giving , , plus the grazing solution (II → Q, III → P).
For (IV), the official key maps (IV → S), the value obtained for . Option (A).
