Question

Study the given ray diagram and select the correct statements from the following:

(A) The device$X$ is a concave mirror and the device $Y$ is a convex lens, whose focal lengths are$20cm$and $25cm$ respectively.
(B) The device$X$is a convex lens and the device$Y$is a concave mirror, whose focal lengths are $20cm$ and $25cm$ respectively.
(C) The device$X$is a concave lens and the device$Y$is a convex mirror, whose focal lengths are $20cm$ and$25cm$ respectively.
(D) The device $X$ is a concave lens and the device $Y$ is a concave mirror, whose focal lengths are $20cm$ and $25cm$ respectively.

Answer 1

Hint We can predict the type of mirror/lens by checking if the rays converge or diverge on the same side of the mirror/lens or on the opposite side of the mirror or lens depending on the distance of the object from the mirror or lens. Also, only convex mirrors and concave lenses are not capable of forming real images.

Complete Step by step solution
Optical device-$X$: As there are no objects seen in the image and the rays seem parallel to each other, it can be inferred that the rays are coming from infinity. Rays that come from infinity will converge or appear to converge to a point when it passes an optical device like a lens or a mirror, the converging point being it’s focal length. In the given figure, the rays come from infinity, pass the optical device, and converge to a point on the screen at a distance $20cm$ from it. This means that it is a lens (as rays pass through the optical device to form real images) with focal length$20cm$. As the image is formed on the other side of the lens, and as the image is real (concave lens always forms virtual image), the lens is a converging lens or convex lens.
Now coming to the optical device- $Y$, the rays are reflected from $Y$ which means that it is a mirror. The rays are coming from infinity in this case as well and they converge to a point on the screen at a distance $25cm$ from the mirror. So the focal length of the mirror is $25cm$. But in this case, the focal point is formed on the same side of the mirror as that of the emerging rays, and a real image is formed. This means that $Y$is a concave mirror as only concave mirrors are capable of forming real images.

$\therefore$ Option (B) is the correct answer

Note
Real images are the images that can be obtained on a screen while a virtual image cannot be obtained on a screen. For similar ray diagrams, always check if the image formed is a real image or a virtual image. This is because convex mirrors and concave lenses are not capable of forming real images, they can only form virtual images; so the answer can be determined easily.