A ray of light falls normally on one of the two shorter faces of a right-angled isosceles glass prism of refractive index 1.5 placed in air. Consider the following statements:
(A) The ray meets the longest face of the prism at an angle of incidence of \( 45^\circ \).
(B) The ray is totally reflected at the longest face, as \( 45^\circ \) is greater than the critical angle for the glass.
(C) The ray comes out of the prism after turning through \( 90^\circ \).
(D) The ray would still be totally reflected at the longest face if the refractive index of the prism were 1.33.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A), (B) and (C) only
A ray that falls normally on a face enters without bending. In a right-angled isosceles prism the longest face is inclined at \( 45^\circ \) to each of the shorter faces. The ray is totally reflected at a glass-air surface only if its angle of incidence there is greater than the critical angle, given by \( \sin i_c=1/n \).
For the glass of refractive index 1.5:
\( \begin{aligned} \sin i_c &= \frac{1}{1.5} \\ &\approx 0.667 \end{aligned} \)
\( \Rightarrow\; i_c\approx41.8^\circ \)
(A) The ray meets the longest face of the prism at an angle of incidence of \( 45^\circ \). — True. The ray goes straight on inside the glass, at right angles to the face it entered. Since the longest face is tilted at \( 45^\circ \) to that face, the angle between the ray and the normal to the longest face is \( 45^\circ \).
(B) The ray is totally reflected at the longest face, as \( 45^\circ \) is greater than the critical angle for the glass. — True. The angle of incidence, \( 45^\circ \), is larger than \( i_c\approx41.8^\circ \). So no light is refracted out, and the whole ray is reflected back into the glass.
(C) The ray comes out of the prism after turning through \( 90^\circ \). — True. Reflection at \( 45^\circ \) turns the ray through \( 180^\circ-2\times45^\circ=90^\circ \). It then meets the other shorter face normally and leaves without further bending.
(D) The ray would still be totally reflected at the longest face if the refractive index of the prism were 1.33. — False. For this material the critical angle is:
\( \begin{aligned} \sin i_c &= \frac{1}{1.33} \\ &\approx 0.752 \end{aligned} \)
\( \Rightarrow\; i_c\approx48.8^\circ \)
The angle of incidence of \( 45^\circ \) is now smaller than the critical angle. So part of the ray is refracted out through the longest face.
NCERT (2026-27):
Total Internal Reflection – “The refractive index of denser medium 1 with respect to rarer medium 2 will be n12 = 1/sin ic. …”
Total Internal Reflection in Nature and Its Technological Applications – “(i) Prism: Prisms designed to bend light by 90° or by 180° make use of total internal reflection …. In the first two cases, the critical angle ic for the material of the prism must be less than 45°. …”