Question

 AN OBJECT 5 cm IN SIZE IS HELD 30 cm AWAY FROM CONVERGING LENS OF RADIUS OF CURVATURE 40 cm .FIND THE POSITION & NATURE OF IMAGE. ​

Answer 1

Answer:

We are given a concave mirror.

Here,

Object size, h = + 5.0 cm

Object distance, u = - 25 cm

Radius of curvature, R = - 30 cm [R is -ve for a concave mirror]

Therefore,

Focal length, straight f space equals space straight R over 2 space equals space minus 15 space cm

Now, using the mirror formula,

1 over straight u plus 1 over straight v space equals space 1 over straight f

we have,

1 over straight v space equals space 1 over straight f minus 1 over straight u space

space space space space space space equals space fraction numerator 1 over denominator negative 15 end fraction space minus space fraction numerator 1 over denominator negative 25 end fraction space

space space space space space space equals space fraction numerator negative 5 plus 3 over denominator 75 end fraction

space space space space space space equals space fraction numerator negative 2 over denominator 75 end fraction

i.e., straight v space equals space minus 37.5 space cm.

Magnification, straight m space equals space fraction numerator straight h apostrophe over denominator straight h end fraction space equals space minus straight v over straight u

therefore Image size, straight h apostrophe space equals space minus fraction numerator v space h over denominator straight u end fraction

equals space minus fraction numerator left parenthesis negative 37.5 space cm right parenthesis thin space left parenthesis plus 5.0 space cm right parenthesis over denominator left parenthesis negative 25 space cm right parenthesis end fraction space

equals space minus 7.5 space cm.

As v is (-)ve, so a real, inverted image of height 7.5 cm is formed at a distance of 37.5 cm in front of the mirror.