Two thin lenses are of same focal length (f), but one is convex and the other is concave. When they are placed in opposite with each other, the equivalent focal of the combination will be:

Question

A light ray passes from air (refractive index = 1) into water (refractive index = 1.33). If the angle of incidence is 30°, what is the angle of refraction in water?

Answer 1

To solve this problem, we need to understand the concept of the equivalent focal length of a combination of lenses. When two lenses are placed in contact with each other, the equivalent focal length \( F \) of the combination can be calculated using the formula:

\(\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2}\)

Here, \( f_1 \) and \( f_2 \) are the focal lengths of the two lenses. In this problem, one lens is convex with focal length \( f \) and the other is concave with the same focal length \( -f \). The negative sign is used for the concave lens as it diverges light rays.

Substituting the given focal lengths \( f_1 = f \) and \( f_2 = -f \) into the formula, we get:

\(\frac{1}{F} = \frac{1}{f} + \frac{1}{-f}\)

Simplifying this equation, we have:

\(\frac{1}{F} = \frac{1}{f} - \frac{1}{f} = 0\)

When \(\frac{1}{F} = 0\), it implies that the equivalent focal length \( F \) is infinite. This is because the reciprocal of infinity is zero. Therefore, the combination does not converge or diverge the light rays, behaving as a plane glass slab.

Hence, the correct answer is: Infinite.

Answer 2