Two transparent media A and B are separated by a plane boundary. The speed of light in medium A is 2.0 x 108 ms-1 and in medium, B is 2.5 x 108 ms-1. The critical angle for which ray of light going from A to B suffers total internal reflection is?

By Ritesh|Updated : November 11th, 2022

(a) sin-1 (½)

(b) sin-1 (⅖)

(c) sin-1 (⅘)

(d) sin-1 (⅗)

The critical angle for which the ray of light going from A to B suffers total internal reflection is sin-1 (⅘). Steps to The critical angle for which the ray of light going from A to B suffers total internal reflection:

Step 1: The necessary inclination for complete internal reflection

  1. The incidence angle above which 100% internal reflection takes place is known as the critical angle.
  2. Different forms of waves, including light waves, electromagnetic waves, sound waves, etc., exhibit total internal reflection.

Step 2: Now we have to calculate the light's velocity ratio in medium A.

nA = c/vA

Here, c denotes the speed of light in air, vA denotes the velocity of light in medium A, and nA denotes the ratio of the velocities of light in medium A.

nA = 3 x 108 ms-1/ 2.0 x 108 ms-1

On simplifying we get

nA = 1.5

Step 3: Now we have to calculate the ratio of the velocities of light in media B.

nB = c/vB

Here, nB is the ratio of the velocities of light in media B, and vB is the velocity of light in media B.

nB = 3 x 108 ms-1/ 2.5 x 108 ms-1

On simplifying we get

nB = 1.2

Step 4: Now we have to calculate the critical angle

The critical angle can be calculated using the formula: sin (ic) = nB/nA

Here, ic is the critical angle

Substituting the values in the formula we get:

sin (ic) = 1.2/1.5

ic = sin-1 (⅘)

The critical angle for 100% internal reflection of the beam is sin-1 (⅘)

Summary:

Two transparent media A and B are separated by a plane boundary. The speed of light in medium A is 2.0 x 108 ms-1 and in medium, B is 2.5 x 108 ms-1. The critical angle for which the ray of light going from A to B suffers total internal reflection is?

Two transparent media A and B are separated by a plane boundary. The speed of light in medium A is 2.0 x 108 ms-1 and in medium, B is 2.5 x 108 ms-1. The critical angle for which ray of light going from A to B suffers total internal reflection is sin-1 (⅘).

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