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
VU

a. 50cmand24

b. 60cmand24

c. 50cmand15

d. 60cmand15

Answer 1

Answer on Question #41498 – Physics – Mechanics

Find the position and magnification, $m$, of the image formed by a concave mirror of focal length $24~\mathrm{cm}$ when an object is placed $40~\mathrm{cm}$ from the mirror given that $m$ is VU

a. 50cmand24

b. 60cmand24

c. 50cmand15

d. 60cmand15

Solution:

$f = 24\mathrm{cm}$ – focal length;

$d_0 = 40\mathrm{cm}$ – distance from object to mirror;

$d_i$ – distance from image to mirror;

$m$ – magnification;

The Gaussian mirror equation, also known as the mirror and lens equation, relates the object distance $d_0$ and image distance $d_i$ to the focal length $f$:

$$\frac{1}{d_0} + \frac{1}{d_i} = \frac{1}{f}$$ $$\frac{1}{d_i} = \frac{1}{f} - \frac{1}{d_0} = \frac{d_0 - f}{f d_0}$$ $$d_i = \frac{f d_0}{d_0 - f} = \frac{24\mathrm{cm} \cdot 40\mathrm{cm}}{40\mathrm{cm} - 24\mathrm{cm}} = 60\mathrm{cm}$$

Fomrula for the magnification:

$$m = \frac{h_{\text{image}}}{h_{\text{object}}} = \frac{d_i}{d_0} = \frac{60\mathrm{cm}}{40\mathrm{cm}} = 1.5$$

Hence, correct answer is d.

**Answer**: d. 60cmand15

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