Question

The expected graphical representation of the variation of angle of deviation '$\delta$' with angle of incidence 'i' in a prism is : 

• A. A
• B. B
• C. C
• D. D

Hint:

The graph of the angle of deviation versus the angle of incidence for a prism is a characteristic curve that first decreases, reaches a minimum, and then increases. This minimum point corresponds to the angle of minimum deviation, a key concept in prism optics.

Answer 1

The Correct Option is D

The relationship between the angle of deviation ($\delta$), the angle of incidence (i), the angle of emergence (e), and the prism angle (A) is given by:
$\delta = i + e - A$.
As the angle of incidence (i) is increased from a very small value, the angle of emergence (e) decreases. The angle of deviation ($\delta$) initially decreases.
The deviation reaches a minimum value, called the angle of minimum deviation ($\delta_m$), at a specific angle of incidence. At this point, the light ray passes symmetrically through the prism, and the angle of incidence equals the angle of emergence ($i=e$).
If the angle of incidence is further increased beyond this point, the angle of deviation starts to increase again.
This behavior results in a characteristic U-shaped curve when $\delta$ is plotted against i. The curve is not a perfect parabola and is not symmetric about the minimum deviation point, but it clearly shows a single minimum.
Looking at the options:
(A) shows a linear increase, which is incorrect.
(B) shows a linear decrease, which is incorrect.
(C) shows a curve with a maximum point, which is incorrect.
(D) shows a U-shaped curve with a distinct minimum, which correctly represents the variation of deviation with the angle of incidence.