Question

Question 2
A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it. Where is the needle placed in front of the convex lens if the image is equal to the size of the object? Also, find the power of the lens.

Answer 1

Image distance, v = 50 cm
We know that, m = $\frac{v}{u}$ ,in case of lens
m = -1 ;as image is real and inverted and equal to the size of the object
-1 = $\frac{50}{u}$
Thus, u = - 50 cm
Object distance, u = - 50 cm
focal length = f
According to the lens formula,
u = - 50 cm
v = + 50 cm
f = ?
$\frac{1}{f}$ = $\frac{1}{v}$ - $\frac{1}{u}$
$\frac{1}{f}$ = $\frac{1}{50}$ + $\frac{1}{50}$

$\frac{1}{f}=\frac{(1+1)}{50}=\frac{2}{50}$
f = + 25 cm

Focal length in metres = 25/100 = 0.25m
Power of lens (P) = $\frac{1}{f}$ = $\frac{1}{0.25}$ = + 4D.