Question

An object 12 cm in front of a convex mirror forms an image 6 cm behind the mirror. Find the focal length of the mirror.

Answer 1

Answer:

Focal length of the given convex mirror is 12cm

Explanation:

Given , distance of object from the convex mirror = 12 cm

Distance of image from the convex mirror  formed behind the mirror  = 6cm

As we know that , object is placed in front of a convex mirror , so the sign of object taken as negative  and image is formed behind the  convex mirror  so , the sign of image  taken as  positive  .

Therefore , v = 6cm , u = -12 cm  

Where , v is the image distance and

u stand for object distance

Now,  from the mirror formula ,

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

Now put the value of v = 6 and u = -12 in the above mirror formula we get,

⇒$\frac{1}{f} = \frac{1}{6} - \frac{1}{12}$

⇒$\frac{1}{f} = \frac{2-1 }{12}$ = $\frac{1}{12}$

⇒f = 12 cm

Hence , focal length of the mirror is 12 cm .

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