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

Answer 1

Answer on Question #41830, 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

Solution:

Given:

$d_{o} = 40~cm = 0.4~m,$

$f = 24~cm = 0.24~m,$

$m = ?$

$d_{i} = ?$

The equation expresses the quantitative relationship between the object distance $(\mathrm{d}_o)$ , the image distance $(\mathrm{d_i})$ , and the focal length (f). The equation is stated as follows:

$$\frac {1}{f} = \frac {1}{d _ {o}} + \frac {1}{d _ {i}}$$

Thus,

$$\frac {1}{d _ {i}} = \frac {1}{f} - \frac {1}{d _ {o}}$$ $$\frac {1}{d _ {i}} = \frac {1}{0 . 2 4} - \frac {1}{0 . 4} = 1. 6 7$$ $$d _ {i} = \frac {1}{1 . 6 7} = 0. 6 m = 6 0 c m$$

The magnification of the lens is given by:

$$m = - \frac {d _ {i}}{d _ {o}}$$ $$m = - \frac {6 0}{4 0} = - 1. 5$$

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

Answer. $d_{i} = 60 \, \text{cm}, m = -1.5$

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