Question

A luminous object is placed at a distance of 30 cm from the convex lens of focal length 20 cm.
On the other side of the lens, at some distance from the lens a convex mirror of radius of
curvature 10 cm be placed so that final image coincide with the object. If a distance of the convex
mirror from the lens is 10 X cm. What is the value of X? Please answer the question with proper steps.​

Answer 1

Answer:

In order to obtain image coincident with object, the image of object after refraction from the convex lens must be formed on the center of curvature of the convex mirror.

Distance of image from convex lens after refraction from it can be found by using lens equation:

⇒

v

1

=

u

1

+

f

1

=

−30

1

+

20

1

⇒v=60cm

Thus, image is formed at a distance of 60cm from the lens.

Thus, the convex mirror should be kept at distance 60cm−10cm=50cm from the lens such that the image is formed at its center of curvature.

Explanation:

hope this will help you

Answer 2

★ Solution :-

As per the given data ,

• Image distance = - 30cm

( image distance is negative as distance is measured from the optical centre of the lens )

• Focal length = + 20 cm

( as focal length of a convex lens is positive )

• The distance of the convex mirror from the lens = 10 X cm

• Radius of curvature of the mirror = 10 cm

According to the question the final image coincides with the object this can happen only if the light passes through the center of curvature of the mirror

By applying the lens formula ,

$\longrightarrow\mathtt{\dfrac{1}{f} = \dfrac{1}{v}-\dfrac{1}{u}}$

here ,

• f = focal length = + 20 cm
• v = image distance = 10X + 10
• u = object distance = -30 cm

$\longrightarrow\mathtt{\dfrac{1}{20} = \dfrac{1}{10x+10}-\dfrac{1}{-30}}$

$\longrightarrow\mathtt{\dfrac{1}{20} = \dfrac{1}{10x+10}+\dfrac{1}{30}}$

$\longrightarrow\mathtt{\dfrac{1}{10x+10}=\dfrac{1}{20} -\dfrac{1}{30}}$

$\longrightarrow\mathtt{\dfrac{1}{10x+10}=\dfrac{3-2}{60} }$

$\longrightarrow\mathtt{\dfrac{1}{10x+10}=\dfrac{1}{60} }$

$\longrightarrow\mathtt{10 x+10=60}$

$\longrightarrow\mathtt{10 x=50}$

$\longrightarrow\mathtt{x = 5 }$

The value of x is 5

The distance of the lens from the mirror = 50 cm