A ray of light falls normally on one face of a prism of refracting angle \( 30^\circ \) and refractive index \( \sqrt{3} \). Consider the following statements:
(A) The ray enters the prism without any bending at the first face.
(B) The angle of deviation of the ray is \( 60^\circ \).
(C) The ray leaves the second face making an angle of \( 60^\circ \) with the normal.
(D) If the refracting angle of the prism were \( 60^\circ \), the ray would not come out of the second face.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A), (C) and (D) only
A ray that falls normally on a face has zero angle of incidence, so it goes in along the normal with \( r_1=0 \). Since \( r_1+r_2=A \), it meets the second face at an angle of incidence \( r_2=A \), that is \( 30^\circ \). Snell’s law at that face gives the angle of emergence:
\( \begin{aligned} \sin e &= \sqrt{3}\,\sin30^\circ \\ &= \frac{\sqrt{3}}{2} \end{aligned} \)
\( \Rightarrow\; e=60^\circ \)
(A) The ray enters the prism without any bending at the first face. — True. At normal incidence \( \sin i=0 \), so \( \sin r=0 \) as well and the ray continues along the normal.
(B) The angle of deviation of the ray is \( 60^\circ \). — False. With \( i=0 \) and \( e=60^\circ \), the deviation is:
\( \begin{aligned} \delta &= i+e-A \\ &= 0+60^\circ-30^\circ \\ &= 30^\circ \end{aligned} \)
(C) The ray leaves the second face making an angle of \( 60^\circ \) with the normal. — True. This is the angle of emergence found above from \( \sin e=\sqrt{3}/2 \).
(D) If the refracting angle of the prism were \( 60^\circ \), the ray would not come out of the second face. — True. The ray would then meet the second face at \( 60^\circ \). For this material, \( \sin i_c=1/\sqrt{3} \), which is about 0.58. So the critical angle is \( i_c\approx35^\circ \). As \( 60^\circ \) is larger than \( i_c \), the ray is totally reflected inside the prism.
NCERT (2026-27):
Total Internal Reflection – “The angle of incidence corresponding to an angle of refraction 90°, … is called the critical angle (ic) for the given pair of media. … For values of i larger than ic, Snell’s law of refraction cannot be satisfied, and hence no refraction is possible.”
Total Internal Reflection – “The refractive index of denser medium 1 with respect to rarer medium 2 will be n12 = 1/sin ic. …”