Question

Distance between object and image is 30 cm by using spherical mirror of found length $\frac{x}{4}$, $m = -\frac{1}{3}$ there find 'x'

• A. 15
• B. 30
• C. 45
• D. 75

Answer 1

Answer: (C)

45

Answer 2

Let the object distance be $u$ and the image distance be $v$. For a concave mirror with a real, inverted image, both the object and image are in front of the mirror, so the distance between them is

$$u - v = 30$$

Given the magnification

$$m = -\frac{v}{u} = -\frac{1}{3}$$

we have

$$v = \frac{u}{3}$$

Substitute:

$$u - \frac{u}{3} = 30 \Rightarrow \frac{2u}{3} = 30 \Rightarrow u = 45 \text{ cm}$$

Then

$$v = \frac{45}{3} = 15 \text{ cm}$$

The mirror formula is

$$\frac{1}{f} = \frac{1}{u} + \frac{1}{v} = \frac{1}{45} + \frac{1}{15} = \frac{1+3}{45} = \frac{4}{45}$$

Thus,

$$f = \frac{45}{4} \text{ cm}$$

Since the focal length is given as $\frac{x}{4}$, equate:

$$\frac{x}{4} = \frac{45}{4} \Rightarrow x = 45$$