Question

Two light beams fall on a transparent material block at point 1 and 2 with angle \( \theta_1 \) and \( \theta_2 \), respectively, as shown in the figure. After refraction, the beams intersect at point 3 which is exactly on the interface at the other end of the block. Given: the distance between 1 and 2, \( d = 4/3 \) cm and \( \theta_1 = \theta_2 = \cos^{-1} \frac{n_2}{2n_1} \), where \( n_2 \) is the refractive index of the block and \( n_1 \) is the refractive index of the outside medium, then the thickness of the block is cm.

Hint:

To solve for the thickness of a block in refractive problems, use Snell's Law and consider the geometry of the refracted beams.

Answer 1

Correct Answer: 3

Using the given equation and considering Snell's Law, we calculate the thickness of the block as 3 cm based on the geometric conditions of the refracted beams. Thus, the correct answer is 3 cm.