Question

An object 6cm high is placed at a distance of 6cm from a convex mirror of radius of curvature 24cm.find the nature ,position and size of the image

Answer 1

Answer:

Explanation : ࿇༲࿆༫࿆࿂࿆༗VI꙰K꙰A꙰S꙰H꙰࿇༲࿆༫࿆࿂࿆༗

Answer 2

Concept:

Mirror Formula=>

1/v+1/u= 1/f

Where:

u is the object distance

v is the image distance

and f is the Focal length and is given by R/2

where R is the radius of curvature.

Magnification Formula=>

M= -v/u = h’/h

Where h’ is image height and h is object height.

Given:

u=-6 cm

R= 24cm

Find:

v and h’

Solution:

F=R/2 i.e., 12cm

Using the Mirror formula

1/v+1/u= 1/f

1/v=1/f-1/u

v= f*u/(u-f)

putting the values gives->

v= 12*(-6)/(-6-12)

v= -72/-18

v= 4 cm

Since the value of v>0 hence the image is behind the mirror and virtual.

Now to find the h’ we use the Magnification formula:

M=-v/u

M=-4/-6=2/3 =0.66..

M is also equal to h’/h hence

h’/h=2/3

h’= h*2/3

h’=6*2/3= 4cm.

The image formed is virtual and erect. Since the value of Magnification(M) <1 hence, the image is smaller than the object.

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