Question

A concave mirror produces three times enlarged virtual image of an object placed at 10 cm in front of it . Calculate the radius of curvature of the mirror .​

Answer 1

$\huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

Given :

• Mirror is Concave
• Object Distance (u) = -10 cm
• Magnification (m) = 3

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To Find :

Radius of Curvature

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Solution :

As we know,

$\Large \displaystyle {\boxed{\rm{m \: = \: \frac{-v}{u}}}}$

Put Values

⇒ 3 = -v/-10

⇒3 = v/10

⇒v = 3 * 10

⇒v = 30 cm

∴ Image distance (v) = 30 cm

$\rule{200}{2}$

And Mirror Formula is :

$\Large \displaystyle {\boxed{\rm{\frac{1}{f} \: = \: \frac{1}{v} \: + \: \frac{1}{u}}}}$

Put Values

⇒ 1/f = 1/30 + (-1/10)

⇒1/f = 1/30 - 1/10

⇒1/f = 1 - 3/30 (Take L.C.M)

⇒1/f = -2/30

⇒f = -30/2

⇒f = -15

∴ Focal Length (f) = -15 cm

$\rule{200}{2}$

Formula for Radius of curvature is :

$\Large \displaystyle {\boxed{\rm{R \: = \: 2f}}}$

Put Values

⇒ R = 2(-15)

⇒R = -30 cm

∴ Radius of Curvature (R) is -30 cm