Question

Find the position and magnification, m, of the image formed by a concave mirror of focal length 24 cm when an object is placed 40 cm from the mirror given that m is V/U

Answer 1

Answer on Question #41823, Physics, Optics

Find the position and magnification, $m$, of the image formed by a concave mirror of focal length 24 cm when an object is placed 40 cm from the mirror given that $m$ is V/U

Solution:

Given:

$$\begin{array}{l} u = 40 \text{ cm}, \\ f = 24 \text{ cm}, \\ v = ? \\ m = ?, \\ \end{array}$$

Mirror formula is the relationship between object distance (u), image distance (v) and focal length.

The mirror formula for a concave mirror is

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

Thus,

$$\frac{1}{v} = \frac{1}{f} - \frac{1}{u}$$ $$\frac{1}{v} = \frac{1}{24} - \frac{1}{40} = \frac{1}{60}$$ $$v = 60 \text{ cm}$$

The magnification of the lens is given by:

$$m = - \frac{v}{u}$$ $$m = - \frac{60}{40} = -1.5$$

A negative sign in the value of the magnification indicates that the image is real.

Answer. position of the image $v = 60$ cm, magnification $m = -1.5$

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