Question

a convex lens throws on a screen 12m from the lens a magnified image of the object. if the magnification is 15, find the focal length of the lens

Answer 1

i guess the ans is 8.57

v=-12cm mag =15
u= -12/15 = -0.8
1/f= 1/v -1/u
=1/0.8-1/12
f= 8.57

Answer 2

Given: A convex lens throws on a screen 12m from the lens a magnified image of the object. The magnification is 15.

To find: Focal length of the lens

Solution: Let the image distance be v, object distance be u and focal length be f.

Here, the lens projects the image 12 m from the lens. Therefore, v = 12 m

Since the image is formed on screen, therefore the image is real. The magnification for real image is negative. Therefore, magnification (m) = -15

The magnification formula for lens is:

m = v/u

=> -15 = 12/u

=> u = -12/15

=> u = -4/5

=> 1/u = -5/4

The lens formula is:

$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$

$= > \frac{1}{f} = \frac{1}{12} - \frac{ - 5}{4}$

$= > \frac{1}{f} = \frac{1 + 15}{12}$

$= > \frac{1}{f} = \frac{16}{12}$

=> f = 12/16

=> f = 0.75 m

Therefore, the focal length of the lens is 0.75 m.