Question

A student focused the image of a distant object using a device ‘X’ on a white screen ‘S’ as shown in the figure. If the distance of the screen from the device is 40cm, select the correct statement about the device.

A. The device X is a convex lens of focal length 20cm.
B. The device X is a concave mirror of focal length 40cm.
C. The device X is a concave mirror of radius of curvature 40cm.
D. The device X is a convex lens of focal length 40cm.

Answer 1

Hint: Knowledge of lenses and mirrors are required to solve this problem. Different conditions and relations between object position and image position is essential. The way the rays change upon interacting with the optical device will give vital information, hence knowledge of how rays coming from objects at different positions interact with different kinds of optical devices, such as glass, lens and mirrors is useful.

Step by step solution:
We know from the question that the object is far away. We can hence, comfortably approximate the object to be at infinity. We will be using the condition of objects being at infinity to solve this problem.

We see that the image is being formed on the other side of the device. Hence, we can remove mirrors from our consideration as the option, because a real image is being formed and that cannot happen for mirrors. For mirrors, reflection will take place, making the image on the same side on which the object is present.

So, we have the option of different kinds of lens available with us for the device.

The two types of lenses are convex or converging lens and concave or diverging lens.
As the name suggests, convex lens causes the rays to converge once the rays pass through the lens. This is what is seen to be happening in the image shown.

Finally, now that we have established the device ‘X’ to be a convex lens, we will use the condition of the object being at infinity. Whenever rays from an object at infinity pass through a convex lens, they converge at the focal length of the lens.

Here, the distance between the device and the screen is given as 40cm.
Hence, the device ‘X’ is a convex lens of focal length 40cm.

Note: We can establish the object is at infinity by looking at the rays of the object as well, since the rays are parallel, they are indicative of the object being at infinity or very far away.
Here, since the rays seem to converge in the image given, hence we discard a normal glass slab as a possible option for the device ‘X’. Since, the rays will only get refracted from the glass slab, however the rays will still continue to remain parallel.