Physics · Optics, Nature of Light and Optical Instruments

To calculate the refractive index of medium Q, we can use Snell's law, which relates the angles of incidence and refraction to the refractive indices of the two media involved.

Snell's law states: n1 * sin(theta1) = n2 * sin(theta2)

Where:

n1 = refractive index of the first medium (in this case, air)

theta1 = angle of incidence in the first medium

n2 = refractive index of the second medium (in this case, medium Q)

theta2 = angle of refraction in the second medium

Given:

Angle of incidence in air (theta1) = 45˚

Angle of refraction in medium Q (theta2) = 30˚

Let's denote the refractive index of medium Q as n2.

Applying Snell's law:

n1 * sin(theta1) = n2 * sin(theta2)

Substituting the known values:

1 * sin(45˚) = n2 * sin(30˚)

Simplifying:

sin(45˚) = n2 * sin(30˚)

Using trigonometric values:

1/√2 = n2 * (1/2)

Rearranging and solving for n2:

n2 = (1/√2) / (1/2)

n2 = 2/√2

n2 = √2

Therefore, the refractive index of medium Q is equal to √2.

This incorrectly inverts the relationship between the angles of incidence and refraction. Snell's law requires the sine of the angle in the first medium to be divided by the sine of the angle in the second medium.

This option correctly applies Snell's law, where the sine of the angle in the first medium (air) is divided by the sine of the angle in the second medium (medium Q).

This option uses incorrect angles for the calculation. The angle of incidence in air is 45˚, not 60˚.

This option uses an incorrect angle for the second medium. The angle of refraction in medium Q is 30˚, not 60˚.