Question

When a monochromatic ray of light is passed through an equilateral glass prism, it is found that the refracted ray in glass is parallel to the base of the prism. If '$i$' and '$e$' denote the angles of incidence and emergence respectively, then}

• A. $i>e$
• B. $i<e$
• C. $i = e$
• D. $i + e = 90^\circ$

Hint:

The refracted ray is parallel to the base of an equilateral prism only in the condition of minimum deviation, where the angles of incidence and emergence are equal ($i = e$).

Answer 1

The Correct Option is C

Step 1: In an equilateral prism, the prism angle is $A = 60^\circ$. The relation between the prism angle and the internal angles of refraction is: \[ A = r_1 + r_2 \]
Step 2: When the refracted ray inside the prism is parallel to the base, the geometry of the light path is symmetric. This indicates that the light is passing through the condition of minimum deviation.
Step 3: For a symmetric path through an equilateral or isosceles prism, the angle of refraction at the first surface ($r_1$) must equal the angle of refraction at the second surface ($r_2$): \[ r_1 = r_2 = \frac{A}{2} = 30^\circ \]
Step 4: According to Snell's Law, if the internal angles are equal ($r_1 = r_2$), then the external angles must also be equal to satisfy the refractive index equation $\mu = \frac{\sin i}{\sin r_1} = \frac{\sin e}{\sin r_2}$: \[ i = e \]