A boy stands and looks at a small source of light on a wall at a distance 360 cm from him. The source is at the same height as his eyes, and his line of sight is perpendicular to the wall. Now, a convex lens of focal length 60 cm is introduced exactly midway between his eyes and the source of light such that the principal axis of the lens is coincident with his line of sight. Assuming that the size of an object perceived by a person is proportional to 1r, where r is the distance between the eyes of the person and the object, the number of times the size of the source of light as perceived by the boy increases due to the introduction of the lens is ________.

Question

A boy stands and looks at a small source of light on a wall at a distance 360 cm from him. The source is at the same height as his eyes, and his line of sight is perpendicular to the wall. Now, a convex lens of focal length 60 cm is introduced exactly midway between his eyes and the source of light such that the principal axis of the lens is coincident with his line of sight. Assuming that the size of an object perceived by a person is proportional to  1r, where r is the distance between the eyes of the person and the object, the number of times the size of the source of light as perceived by the boy increases due to the introduction of the lens is ________.

Accepted Answer

Initially, the boy looks at the source directly After the introduction of the lens, the boy no longer looks at the source itself, but looks at the image of the source formed by the lens For the position of the image:
$\frac{1}{v} = \frac{1}{f} + \frac{1}{u} = \frac{1}{60} + \frac{1}{- 180} \Rightarrow v = 90 c m$
So, the image is at a distance 180 – 90 = 90 cm from the boy
Now, the image itself is M times the size of the source of light, where
$M = | \frac{v}{u} | = \frac{1}{2}$
Since the perceived size is proportional to $\frac{1}{r}$ , the final size of the image as perceived by the boy is $\frac{(\frac{1}{90})}{(\frac{1}{360})} (\frac{1}{2}) = 2$ times the size initially perceived

Best Courses for You

Detailed Solution

courses

Get Expert Academic Guidance – Connect with a Counselor Today!

best study material, now at your finger tips!

download the app

Download the App