Question

If the power of a lens is + 0.1 D and if an object of size 2 m is placed 5 m before the lens. Find the size and position of the image formed?

• A. Image size = 4 cm, image distance = – 10 cm
• B. Image size = 10 cm, image distance = – 4 cm
• C. Image size = 5 cm, image distance = 4 cm
• D. Image size = 4 cm, image distance = 5 cm

Answer 1

The correct option is (A) Image size = 4 cm, image distance = – 10 cm

Step 1, Given data

Power, $P=0.1D$
Object distance, $u=-5m$
Let $v$ be the image distance and $f$ be the focal length.

Step 2, Finding the size and position of the image

We know,
P = $\frac{1}{f}$

Putting all the values

f = 10 m
Now,
Using lens formula,
$\frac{1}{v}$ - $\frac{1}{u}$ = $\frac{1}{f}$

Putting all the values

$\frac{1}{v}$ - $\frac{1}{(-5)}$ = $\frac{1}{\left(10\right)}$ ⇒ $\frac{1}{v}$ = $\frac{1}{10}$ = $\frac{-1}{10}$

v = - 10 m
According to the question
Height of object, $h=2m$
Let $h^{\prime }$ be height of object.

We know that the magnification is given as
m = $\frac{v}{u}$ = $\frac{h^{\prime }}{h}$ ⇒ $\frac{-10}{(-5)}$ = $\frac{h^{\prime }}{2}$

$h^{\prime }$ = 4 m

Hence the Image height = 4 m