Question

Imagine that a spherical mirror gives an image magnified 5 times at a distance 5m.if so determine whether the mirror is concave or convex .how much will be the focal length of the mirror

Answer 1

focal length of concave mirror is 1.25 m

it's concave mirror because image is magnified 5 times of object.

image distance, v = 5m

object distance = u

magnification = -v/u

⇒5 = -5/u

⇒u = - 1m

now using formula, 1/v + 1/u = 1/f

⇒1/5 + 1/-1 = 1/f

⇒1/5 - 1 = 1/f

⇒1/f = -4/5

⇒f = -5/4 = -1.25 m

hence, focal length of concave mirror is 1.25 m

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Answer 2

The focal length of the concave mirror is 1.25 m.

Explanation:

Given that,

Image distance = 5 m

Magnification = 5

We need to calculate the object distance

Using formula of magnification

$m=\dfrac{v}{u}$

Put the value into the formula

$u =\dfrac{5}{5}$

$u=1\ m$

We need to calculate the focal length

Using formula of mirror

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

Put the value into the formula

$\dfrac{1}{f}=\dfrac{1}{5}-\dfrac{1}{1}$

$\dfrac{1}{f}=-\dfrac{4}{5}$

$f=-1.25\ m$

Hence, The focal length of the concave mirror is 1.25 m.

Learn more :

Topic : Spherical mirror

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