Question

An object placed in front of a convex mirror of radius 20cm produces an erect image which is one-fifth the size of the object. How far is the object from the mirror?
20 cm
30 cm
40 cm
50 cm

Answer 1

Answer on question #52721, Physics, Optics

Question An object placed in front of a convex mirror of radius 20cm produces an erect image which is one-fifth the size of the object. How far is the object from the mirror?

20 cm

30 cm

40 cm

50 cm

Solution Focal length of the mirror is $f=R/2=10$ cm. The magnification is

$M=\frac{h_{i}}{h_{o}}=\frac{1}{5}$

so we know that $d_{i}=-d_{o}/5$ now we can use mirror equation to find $d_{o}$ - distance of object.

$\frac{1}{f}=\frac{1}{d_{o}}-\frac{5}{d_{i}}=-\frac{4}{d_{o}}$

$d_{o}=4f=4\cdot 10=40\,cm$

Answer is 40 cm.