Question

AN OBJECT OF 5.0CM IN LENGTH IS PLACED AT A DISTANCE OF 20CM IN FRONT OF A CONVEX MIRROR OF RADIUS OF CURVATURE 30 CM
FIND THE POSITION OF THE IMAGE, ITS NATURE AND SIZE.​

Answer 1

Answer:

Given,

h(height of object)=5cm

u(distance of object)= -20cm

R=30cm

f=R/2=30/2=15cm

By lens formula;

1/f=1/v+1/u

1/v=1/f-1/u

1/v=1/15+1/20

1/v=4+3/60

1/v=7/60

v=60/7 cm=8.56cm

As, m=v/u=h'/h

=60/-20

= -3

so, h'=-v×h/u

=-60×5/-20×7

=15/7

=2.14cm

hence, image is virtual and erect.

Answer 2

answer: position of image is 8.56 cm which is virtual and erect.

and height is 2 cm : diminished

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explanation:

given,

u= -20 cm

R= 30 cm ; f= R/2 = 15 cm

h1= 5 cm

mirror formula,

1/u + 1/v = 1/f

1/v = 1/f - 1/u

1/v = 1/15 - 1/ -20

= 1/15 + 1/20

= 7/60

therefore,

v = 60/7 cm = 8.56 cm (position of image)

again, m= -v/u

= -8.56/-20

= 0.4 cm

and m= h1/h2

h2 =0.4×5= 2 cm