Question

An optical device has been given to a student and he determines its focal length by focusing the web of the sun on a screen placed 24 cm from the device on the same side of the sun.
(i)Name the optical device.
(ii) Find its focal length.

Answer 1

Hint: The mirrors and lenses which are used to focus onto something are called spherical mirrors and lenses as they are a part of some sphere that is cut. These are collectively called optical devices. Real images can only be produced by a concave mirror and convex lens.

Formula used:
$\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}$

Complete step by step answer:
In order to get the answer to the first part of the question, we can use the fact that the screen is placed on the same side of the sun. This can only be the case of a mirror as in a mirror, the rays get reflected and hence the image is formed on the same side of the object. Now, as we have concluded that the device is a mirror, let’s apply mirror formula to find respective focal length:
$\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}$
Since the screen is on the same side, v=-24cm and sun is very far, so $u=-\infty$.
$\implies \dfrac1f = \dfrac{1}{-24} + \dfrac{1}{-\infty}$
Or f = -24 cm.
Hence the answer to (ii) part of the question is f = -24 cm.
Now, since the focal length is negative, therefore it’s a concave mirror.

Also, from the figure, we can see that when the rays from infinity fall on a concave mirror, it gets focused on the focus of the mirror.

Additional information:
One might wonder that the distance of the sun is not infinity but a known finite value. Then why do we consider it to be at infinity? It’s because, in optics, we consider that value to be infinity which is very large as compared to the size of optical devices.

Note:
In addition to this, if it were given that the image is formed on the opposite side i.e. the optical device is in the middle of the screen and object, then it would definitely be the case of refraction through spherical lens. And that also, if the optical device is used to focus on the screen, it could only be the case of a convex mirror.