Question

A student used a device $\left( X \right)$ to obtain/focus the image of a well illuminated distant building on a screen $\left( S \right)$ as shown in the diagram. Select the correct statement about the device $\left( X \right)$.
A) This device is a concave lens of focal length $8$cm.
B) This device is a convex mirror focal length $8$cm.
C) This device is a convex lens of focal length $4$cm.
D) This device is a convex lens of focal length $8$cm.

Answer 1

Hint: You can see that the well illuminated building is the source here. The student uses a device to obtain lights from a distant object on a screen. So, here you should get a hunch that there is a process of convergence happening again and again as the lights are seen on the screen, so you should understand that the image is obviously real.

Step by step answer:
Given:
The object is a distance apart from both the device $\left( X \right)$ and the screen $\left( S \right)$.
From the figure it is evident that the object and the screen hence the image are on different sides of the device.
The distance from the device and the screen is $8cm$.
Step 1:
For the first option, you can easily see that the device $\left( X \right)$ can not be a concave lens as here the converging effect is seen. So option (A) can not be a correct option.
Step 2:
Through Convex lenses will converge the light but the image then would have been on the same side of the object. But you can see from the figure that it is not the case.
Hence, option (B) can not be a correct option.
Step 3:
Convex Lens will converge the lights from a distant source and create a real image but only on the points in its focal plane. Here you can see , the image formed beyond the focal length would be an imaginary one. You can not expect an imaginary image to be projected on a screen.
Hence the option (C) can not be a correct option.
Step 4:
The lights from a distant building falling on a convex lens will converge on the points of the focal plane of the lens and hence the image will be real. So, as the distance between the screen and the device is $8cm$, the screen should be on its focal plane and hence you can understand that the focal length of the convex lens can be nothing but $8cm$.So the option (D) should be the appropriate answer.

Final answer:The correct statement about the device $\left( X \right)$ is (D) The device is a convex lens of focal length $8cm$.

Note:Many of you may miss the two crucial points and befooled with the close options. The object and image are on opposite sides of the device that can not be the convex mirror and again the image being real, the focal length can be nothing but $8cm$.