Question

A screen is placed at 90 cm away from the object. The image of the object on the screen is formed by a convex lens at two different locations separated by 20 cm. What is the focal length of the lens?
A. 42.8 cm
B. 21.4 cm
C. 10.7 cm
D. 5.5 cm

Answer 1

Hint: Here, we can simply find out the focal length of the lens by using the formula. We are given the distance between the screen and the object as well as the distance between two locations of the images with which we can simply find out the focal length of the lens.

Complete Step-by-Step solution:
We are given with the distance between the screen and the object D=90 cm
Distance between the two locations of the convex lens d= 20 cm
$\therefore $ It can be simply solved by using the formula
$ \Rightarrow f = \dfrac{{{D^2} - {d^2}}}{{4D}}{\text{ , where}}$
f is the focal length of the lens
D is the distance between the object and the screen
d is the distance between the two locations of the convex lens
$\therefore $ Applying the formula, we get
$
   \Rightarrow f = \dfrac{{{{90}^2} - {{20}^2}}}{{4 \times 90}} \\
    \\
 $
$ \Rightarrow f = \dfrac{{8100 - 400}}{{360}}$
$ \Rightarrow f = \dfrac{{7700}}{{360}}$
$ \Rightarrow f = 21.4{\text{ cm}}$
$\therefore$ Option B is the correct answer.

Note- We should know the proper definition of the focal length. It states that focal length is the measurement of the distance from the center of a lens to the point at which its image is focused. The longer the distance, the longer the lens. The longer the lens, the more telephoto it is considered.