Question

a convex mirror has radius of curvature 40 cm find the position and size of the image when an object is placed 80 cm in front of the mirror

Answer 1

Given:-

• Radius of Curvature (r) = -40cm

• Object Distance (u) = -80cm

To Find:-

• Position and the size of the image .

Solution:-

We have to find the position and size of the image .Firstly we find the Focal length of mirror.

As we know that Relation between focal length (f) and radius of curvature .

⟹ f = r/2 where r is the radius of curvature

Putting the values ,we get

⟹ f = -40/2

⟹ f = -20 cm

And by using mirror formula

⟹ 1/v + 1/u = 1/f

⟹ 1/v + 1/(-80) = 1/(-20)

⟹ 1/v = 1/80 - 1/20

⟹ 1/v = 1/80 - 4/80

⟹ 1/v = -3/80

⟹ v = -80/3 cm.

Therefore, the image Distance is -80/3 cm .

And now, we have to calculate magnification

⟹ m = -v/u

⟹ m = -(-80/3)/80

⟹ m = 26.66/80

⟹m = 0.33 cm

Thus the magnification of the object is 0.33cm cm.Thus ,the image is erect.