Question

An object is placed at a certain distance on the principal axis of a concave mirror. The image is
formed at a distance of 30 em from the mirror Find the object distance if radius of curvature R
15 cm
a) 15 cm
b) 10 cm c) 30 cm
d) 7.5 cm​

Answer 1

PLS SEE THE ATTACMENT....

Answer 2

Given :-

• Radius of curvature (R) = - 15 cm (concave mirror )
• Image distance (v) = + 30 cm or - 30 cm ( As the position of the image is not mentioned )

To find :-

• Object distance (u)

How to solve :-

• First we need to find the focal length (f) of the mirror
• Then, simply use the mirror formula to find u

Solution :-

We know that ,

➝  f = R / 2

➝  f = 15 / 2

➝  f = 7 .5 cm

Case I : v = + 30 cm

Now , by using mirror formula ,

➝  1 / f = 1 / v + 1 / u

➝   1 / u = 1 / f - 1 / v

➝   1 / u = - 1 / 7.5 -  1 / 30

➝   1 / u = - 4 - 1 / 30

➝   1 / u = -5 / 30

➝   u = - 30 / 5

➝  u = - 6 cm

Case II : v = - 30 cm

Now , by using mirror formula ,

➝   1 / f = 1 / v + 1 / u

➝   1 / u = 1 / f - 1 / v

➝   1 / u = - 1 / 7.5 -  1 /- 30

➝   1 / u = - 4 + 1 / 30

➝   1 / u = -3 / 30

➝   u = - 30 / 3

➝   u = - 10 cm

Hence the image is placed at a distance of 30 cm in front of the mirror