Question

Find the focal length of the concave mirror that produces 4 times larger real image of an object held at 5 cm from the mirror

Answer 1

Explanation:

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Answer 2

4cm is the focal length.

Given,

The magnification m = -4(image is inverted).

Distance between the object and the mirror = 5cm.

To Find,

The focal length of the concave mirror.

Solution,

Given that, the image size is four times bigger than an object.

And the object is 5cm far from the mirror.

So, the magnification value m = -v/u, i.e. -4.

-v/u = -4.

-v/(-5) = -4

-v = 20, v = -20.

To find the focal length use the mirror equation,

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

$\frac{-1}{20}+ (\frac{-1}{5})$ = $\frac{1}{f}$

$\frac{1}{f}$ = $\frac{-1}{20} - \frac{1}{5}$

$\frac{1}{f}$ = $\frac{-20 - 5}{20*5}$

$\frac{1}{f}$= $\frac{25}{100}$

f = $\frac{100}{25}$

f = 4cm.

Hence, 4cm is the focal length of the concave mirror.    

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