Question

An object is placed at a certain distance on the principal axis of concave mirror. The image is formed at
a distance of 30 cm from the mirror. Find the object distance if r= 15 cm
A 15 cm
B) 20 cm
C) 10 cm
D) 7.5 cm
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Answer 1

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Given that

image distance, v= -30 cm

Focal length f= R/2 =- 15/2=-7.5 cm

Use Gaussian formula: (1/u) + (1/v) =(1/f). This gives

(1/u) -(1/30)=-(1/7.5) gives (1/u) =0.033–0.133=-0.1

Therefore, object distance , u = -10 cm

Note: if we take v=30 cm, then u will be - 6.02 cm. As we have taken v positive, u has been found to be less than focal length.

Explanation:

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Answer 2

Answer :

• Object distance is -10

Given :

• An object is placed at a certain distance on the principal axis of concave mirror. The image is formed at a distance of 30 cm from the mirror.
• r = 15cm

To find :

• Find the object distance if r= 15 cm

Solution :

Given,

• Image distance (v) = 30cm
• Radius of curvature (r) = 15cm
• Focal length (f) = r/2 = 15/2 = 7.5cm

As we know that

• 1/f = 1/v + 1/u

Where,

• f is focal length
• v is image distance
• u is object distance

↝ 1/f = 1/v + 1/u

↝ 1/7.5 = 1/30 + 1/u

↝ 1/u = 1/7.5 - 1/30

↝ 1/u = 0.5 - 2 / 15

↝ 1/u = -1.5 / 15

↝ 1/u = -1/10

↝ u = -10

Hence,

Object distance is -10.