Optics#0

Electricity and Magnetism Level 2

A concave mirror gives an image 3 times the size of the object when it is placed at a distance of 20 cm from it. For the image to be real, the focal length should be (in cm)


The answer is 15.

Aakhyat Singh by Aakhyat Singh , 20, India

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1 solution

Rishu Jaar
Nov 3, 2017

Here, M a g n i f i c a t i o n , m = h i h o = 3 = v u Magnification, m=\dfrac{h_i}{h_o}=3=\dfrac{v}{u} ⇒ v = 3 u \Rightarrow v=3u (Please note that v and u are of same sign as the image is real,hence their ratio is positive.) \color{#3D99F6}{\text{(Please note that v and u are of same sign as the image is real,hence their ratio is positive.)}}

Now put v = 3 u v=3u in the mirror formula → \rightarrow

1 v + 1 u = 1 f \large \dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f} ⇒ 1 3 u + 1 u = 1 f \large \Rightarrow \dfrac{1}{3u} +\dfrac{1}{u}=\dfrac{1}{f}

Solving, we get → \rightarrow f = 3 u 4 = 3 4 ⋅ ( − 20 ) = − 15 c m \large\color{#D61F06}{f=\dfrac{3u}{4}=\dfrac{3}{4}\cdot(-20)=-15cm} The negative sign just represents that it’s a concave mirror, and hence the answer is : \large\text{The negative sign just represents that it's a concave mirror, and hence the answer is :} 15 \large\color{#69047E}{\boxed{15}}

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This problem should be under the Classical Mechanics section. @Aakhyat Singh @Calvin Lin sir.

Rishu Jaar - 3 years, 7 months ago

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