A point source of light is kept at a distance of 30 cm, in front of a convex lens of focal length 20 cm. On the other side a concave lens is placed at 10 cm from the convex lens, such that the final rays become parallel to the principal axis. ThenOne/More correct answer(s)A.The focal length of the concave lens is 50 cmB.The focal length of the concave lens is 60 cmC.If the point source of light is kept at 20 cm, the second image will be formed at 50 cm from the concave lensD.If the point source of light is kept at 20 cm, the second image will be formed at infinity

The light from the point source first passes through the convex lens. Using the lens formula, 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance, we can find the image distance from the convex lens. Here, f = 20 cm (convex lens), u = -30 cm (object is on the same side as the light source). Solving, we get v = -60 cm. This means the image is formed 60 cm on the same side as the light source.

This image now acts as the object for the concave lens. The distance of the object from the concave lens is 60 cm (image from convex lens) - 10 cm (distance between lenses) = 50 cm.

We know that the final rays are parallel to the principal axis. This means that the image is formed at infinity. For a concave lens, the image is always formed on the same side as the light source. Therefore, using the lens formula again with f being the focal length of the concave lens, u = -50 cm, and v = ∞, we find that f = -50 cm.

So, the correct answer is A. The focal length of the concave lens is 50 cm.

For options C and D, if the point source of light is kept at 20 cm, the image from the convex lens would be at -40 cm (using the lens formula). This would then be 30 cm from the concave lens. Using the lens formula again, the image from the concave lens would be at infinity. So, the correct answer is D. If the point source of light is kept at 20 cm, the second image will be formed at infinity.

The problem involves two lenses, a convex lens and a concave lens.

Step 1: First, we need to find the image formed by the convex lens. The object is 30 cm in front of the convex lens. Using the lens formula 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance, we can find the image distance.

For the convex lens, f = 20 cm and u = -30 cm (the negative sign indicates that the object is on the same side of the lens as the light is coming from). Substituting these values into the lens formula, we get 1/v = 1/20 - 1/(-30) = 1/20 + 1/30 = 1/12. Therefore, v = 12 cm.

This means the image formed by the convex lens is 12 cm on the other side of the lens.

Step 2: Next, we need to find the image formed by the concave lens. The object for the concave lens is the image formed by the convex lens, which is 12 cm from the convex lens, or 2 cm from the concave lens (since the concave lens is 10 cm from the convex lens).

We know that the final rays are parallel to the principal axis, which means the image is at infinity. Therefore, the image distance v for the concave lens is infinity.

Using the lens formula again, this time for the concave lens, we have 1/f = 1/v - 1/u. Substituting v = infinity and u = -2 cm (the negative sign indicates that the object is on the same side of the lens as the light is coming from), we get 1/f = 0 - 1/(-2) = 1/2. Therefore, f = 2 cm.

However, since the lens is concave, its focal length is negative, so the focal length of the concave lens is -2 cm.

So, none of the options A, B, C, and D are correct.