Question

A mirror forms an image which is 30 cm from an object and twice its height.

(a) Where must the mirror be situated?
(b) What is the radius of curvature?
(c) Is the mirror convex or concave?

Answer 1

 Given, v - u = 30 cm
Magnification 'm' = 2  

`m=(-v)/u` 

⇒ `2=(-v)/u` 

⇒ `v=-2u `  

By puting the value of `V` in the above question we get   

`-2u-u=30` 

⇒ `-3u=30` 

`u=(-30)/3=-10 cm` 

Therefore, the object is situated at a distance of 10 cm from the lens. Hence, the mirror is at a distance of 10 cm from the object.Therefore, distance of the image 'v'=−2×−10 =20 cm

(b)Using the mirror formula, we get 

`1/f=1/v+1/u` 

⇒ `1/f=1/20+1/(-10) `⇒ `1/f=(-10)/200` 

⇒` 1/f=(10-20)/200` 

⇒` 1/f=(-1)/20` 

⇒ `f=-20 cm ` 

 Radius of the curvature R=2 f                                    R =2×−20                                           R=−40 cm  

Thus, the radius of the lens of the lens is 40 cm 

 (c)Since the focal length shows  a negative value, the given mirror is concave.  

m=vu ⇒ 2=Vu

⇒ =2u By Puting the value of `V` in the above quation , we get -2u 

`u=30 

`⇒-3u=30`

`u=30=10` cm 

Therefore, the object is situated at a distance of 10 cm from the less 

Hence the mirror is at a distance of 10 cm from the object therfore, distance of the image

`V=2xx-10=20 ` cm  

R=40cm  Thus, the reduis of  curvature of the lens is 40cm