Question

A converging mirror with a radius of 20cm creates a real image 30cm from the mirror.What is the object distance?
A: -5.0cm
B: -1.5cm
C: -15cm
D: -20cm​

Answer 1

Your answer is option C

Radius of mirror = Radius of curvature

f = R/2 cm

f = 10 cm

Now,

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

u = 30 cm

$\frac{1}{30} + \frac{1}{v} = \frac{1}{10}$

$\frac{1}{30}-\frac{1}{10} = \frac{1}{v}$

$\frac{10-30}{300}$ = $\frac{-20}{300} = \frac{1}{v}\\ \\ v = \frac{-300}{20}\\ \\ = -15 cm$

Hope it helps :)

Answer 2

Answer:

Given that:

Radius of curvature (R) = - 20 cm

Image distance (v) = -30 cm

Focal length of the concave mirror (f) = R/2 = - 20/2 = - 10 cm

Use mirror formula:

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

$\frac{1}{ - 10} = \frac{1}{ - 30} + \frac{1}{u}$

$\frac{1}{u} = \frac{ - 1}{10} + \frac{1}{30}$

$\frac{1}{u} = \frac{ - 3 + 1}{30}$

$\frac{1}{u} = \frac{ - 2}{30}$

$u = \frac{ - 30}{2} = - 15 \: cm$

Hope you got your answer

Have a great day ahead