Question

An object is placed at a certain distance on the principal axis of a concave mirror. The image is formed at a distance of 30cm from the mirror. Find the object distance if radius of curvature R=15cm.​

Answer 1

Answer:

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Answer 2

Given:

Image distance v = 30cm

Radius of curvature R = 15cm

To Find:

Object distance u

Solution:

focal length f = R/2 = 15/2 cm

Mirror formula,

⇒  $\frac{1}{f}$ = $\frac{1}{v}$ + $\frac{1}{u}$

⇒  $\frac{1}{\frac{15}{2} }$ =  $\frac{1}{30}$ + $\frac{1}{u}$

⇒  $\frac{2}{15}$ =  $\frac{1}{30}$  + $\frac{1}{u}$

⇒  $\frac{2}{15}$ -  $\frac{1}{30}$  = $\frac{1}{u}$

⇒  $\frac{4-1}{30}$  =$\frac{1}{u}$      (taking L.C.M of 15 and 30)

⇒  $\frac{3}{30}$  = $\frac{1}{u}$

⇒  $\frac{1}{10}$ = $\frac{1}{u}$

⇒  u = 10cm

So,  the object distance is 10cm.