Question

a convex mirror has a radius of curvature 30cm.find the position and size of image formed if an object of height 5 cm is placed at 10cm from the mirror also draw ray diagram.
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Answer 1

Answer:

Here, The position of the Image is 6cm behind the mirror and its height is 3cm.

Explanation:

Here, As per our question,

As The given mirror is Convex,

=Radius of Curvature of the mirror(R)=30cm

=Height of the object(ho)=5cm

=Distance of object from the mirror(U)=10cm

=Distance of the image from the mirror(V)=?

So, At first we would find out focal length(f) of the mirror, =f=R/2

=f =30/2

=f =15cm

Here, focal length of the mirror is 15cm.

Now, we would find out V of the mirror,

=1/f=1/V+1/U

=1/15=1/V+1/(-10) (As value of U is always negative)

=1/15+1/10=1/V

=1/V=(2+3)/30 (After taking LCM and solving it)

=1/V=5/30

On doing Reciprocal on both sides, we get,

=V=30/5

=V=6cm

Here, The value of V=(+), Thus, the position of the image is 6cm behind the mirror or at right side of the mirror.

Now, Magnification of the mirror(M)=(-V)/U

=M=(-6)/10

=M=(-3)/5

=M=(-0.6)

=M=0.6

So, Height of the image (hi)=

=M=hi/ho

=hi/5=0.6

=hi=0.6×5

=hi=3cm

Hence, Height of the image is 3cm.

Thank you.