Question

An illuminated bulb and a screen are placed $90cm$ apart. What is the focal length of the lens required to produce a real image twice the size of object, on the screen?

• A. $f=-20cm$
• B. $f=-10cm$
• C. $f=20cm$
• D. $f=10cm$

Answer 1

The correct option is C $f=20cm$

Given:
Distance between object and image, $d=90cm$
Magnitude of magnification, $|m|=2$
Image is real

As the image is real, the lens must be a convex lens and it should be placed between object and screen.
Let the object distance be $-u$.
Then the image distance will be $90-u$.

Using formula for magnification,
$m=\frac{v}{u}$
$-2=\frac{90-u}{-u}$
New cartesian sign convention used here.
$u=30cm$

Object distance, $u=-30cm$
Image distance, $v=-2u=60cm$

By lens formula,
$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
$\frac{1}{f}=\frac{1}{60}-\frac{1}{(-30)}$
$f=20cm$