Question

An object 20mm high is placed 10cm from a sperical mirror and forms a virtual image which is 40mm high. what is the radius of curvature off the mirrors​

Answer 1

R = 40 cm

Step-by-step explanation:

From the formulae of magnification:

`(q)/(p)=(image\ height)/(object\ height)\\\\(q)/(10\ cm) = (4\ cm)/(2\ cm)\\\\q = (10\ cm)(2)\\\\q = 20\ cm`

where,

q = image distance from mirror

p = object distance from mirror

Using thin lens formula:

`(1)/(f)=(1)/(p)+(1)/(q)\\\\(1)/(f)=(1)/(10\ cm)+(1)/(-20\ cm)\\\\(1)/(f) = 0.05\\\\f = 20\ cm`

q is negative for the virtual image.

Now, the radius of the spherical mirror is double the focal length (f):

R = 2f

R = 2(20 cm)

R = 40 cm