Question

A convex mirror has its radius of curvature 20 cm. Find the position of the image of a object placed at a distance of 12 cm from the mirror.

Answer 1

Answer :-

Position of the image is 5.45 cm on the right of the mirror .

Explanation :-

We have :-

→ Radius of curvature (R) = 20 cm

→ Distance of the object (u) = 12 cm

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Firstly, let's calculate the focal length of the mirror :-

⇒ f = R/2

⇒ f = 20/2

⇒ f = 10 cm

According to sign convention, we have :-

• u = -12 cm

• f = + 10 cm

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Now, from mirror formula :-

1/v + 1/u = 1/f

⇒ 1/v = 1/f - 1/u

⇒ 1/v = 1/10 - (-1)/12

⇒ 1/v = (6 + 5)/60

⇒ 1/v = 11/60

⇒ 11v = 60

⇒ v = 60/11

⇒ v = 5.45 cm

Answer 2

Answer :-

• Image distance is 60/11 cm, image is formed on the right side of the mirror as v is negative and it is a virtual image.

Explanation :-

Given :

• Object distance (u) = -12 cm
• Radius of curvature (R) = 20 cm

To find :

• Image distance (v)

Solution :

Using the formula :

• 1/u + 1/v = 2/R

Where,

• u = Object distance
• v = Image distance
• R = Radius of curvature

Substituting the values,

→ 1/v = 2/R - 1/u

→ 1/v = 2/20 - 1/-12

→ 1/v = 11/60

→ v = 60/11 cm

• Image is formed on the right side of the mirror as v is negative and it is a virtual image.

Learn more :

Mirror formula :

• 1/f = 1/u + 1/v

We know :

• R = 2f
• 1/f = 2/R

So we get :

• 2/R = 1/u + 1/v