Question

find the distance of the image when an object is placed on the principal axis at a distance of 10cm in front of a concave mirror whose radius of curvature is 8cm

Answer 1

Radius of curvature =8

Focal length f=R/2=8/2=4cm

Object distance (u) =10cm

Image distance(v) =?

We know that mirror formula

1/f=1/u+1/v

1/4=1/10+1/v

1/v=1/4-1/10=5-2/20=3/20=v=20/3cm

Answer 2

Given:

• The object distance = - 10 cm
• The radius of curvature = 8 cm

To Find:

• The image distance.

Solution:

First, we are finding the focal length, f

R = 2f

f = R/2 = 8/2

f = 4 cm = -4 cm { focal length is negative for a concave mirror}

Now using the mirror formula,

1/f = 1/v+1/u → {equation 1}

Rearranging equation 1 interms of image distance.

1/v = 1/f-1/u → {equation 2}

On substituting the given values in equation 2 we get,

⇒ 1/v = - 1/4 + 1/10

We are taking LCM of 4 and 10, which is 20.

⇒ 1/v = (-5+2)/20 {subtracting the terms}

⇒ 1/v = -3/20 {inversing the fractions on both sides}

⇒ v = - 20/3  cm

∴ The image distance = -20/3 cm