Question

A ray of light travels from an optically denser to rarer medium. The critical angle for the two media is \( C \). The maximum possible deviation of the ray will be:

• A. \( \frac{\pi}{2} - C \)
• B. \( 2C \)
• C. \( \pi - 2C \)
• D. \( \pi - C \)

Hint:

When light travels from a denser to a rarer medium, the critical angle is the angle of incidence at which total internal reflection occurs. The maximum deviation of the ray is given by \( \pi - 2C \).

Answer 1

The Correct Option is C

When a ray of light travels from an optically denser medium to a rarer medium and the angle of incidence exceeds the critical angle C, total internal reflection occurs. The maximum possible deviation of the ray occurs when the angle of incidence is equal to the critical angle C.

In such a case, the angle of refraction is \(90^\circ\) as per the definition of the critical angle (since sin\(90^\circ = 1\)). The deviation \(D\) is then given by the formula:

\(D = \text{Angle of incidence} - \text{Angle of refraction}\)

Here, the angle of incidence is \(C\) and the angle of refraction is \(90^\circ\). Therefore, the deviation \(D\) can be calculated as:

\(D = C - 90^\circ\)

Considering that a complete angle is \( \pi \), the actual deviation in terms of \(\pi\) radians is:

\(D = \pi - (\pi/2 + C)\)

Simplifying this gives:

\(D = \pi - C - \pi/2\)

Further simplification results in:

\(D = \pi - 2C\)

Thus, the maximum possible deviation of the ray is \( \pi - 2C \).

Answer 2

We are given that the ray of light travels from an optically denser to a rarer medium. The critical angle for the two media is denoted as \( C \). The maximum possible deviation occurs when the angle of incidence is at the critical angle, as beyond the critical angle the light will undergo total internal reflection. 
Step 1: Understanding the critical angle 
The critical angle \( C \) is the angle of incidence in the denser medium, beyond which total internal reflection occurs. The refracted ray will no longer emerge from the surface and instead be totally reflected inside the denser medium. 
Step 2: Maximum deviation formula 
The maximum possible deviation occurs when the angle of incidence is at the critical angle \( C \). The deviation is the difference between the angle of incidence and the angle of refraction. For a ray moving from a denser medium to a rarer medium, the maximum deviation occurs at twice the critical angle: \[ \text{Maximum deviation} = \pi - 2C \] This formula gives the maximum possible deviation of the ray. Thus, the maximum possible deviation of the ray is \( \pi - 2C \).