A convex lens of focal length 20 cm is placed coaxially with a convex mirror of radius of curvature 20 cm. The two are kept at 15 cm apart from each other. A point object lies 60 cm in front of the convex lens. Draw a ray diagram to show the formation of the image by the combination. Determine the nature and position of the image formed.

Question

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Answer 1

Lens formula for convex lens,

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$

$\frac{1}{v} - \frac{1}{- 6 0} = \frac{1}{2 0}$

$v = 30 c m$

Image ( $I_{1}$ ) formed by the convex lens acts as an object for the convex mirror.

Since the mirror and lens are separated by 15 cm, distance between $I_{1}$ and mirror is 15 cm.

i.e. $u = 15$

For convex mirror,

$f = \frac{R}{2} = 10 c m$

From mirror equation,

$\frac{1}{v _{2}} + \frac{1}{u _{2}} = \frac{1}{f _{2}}$

$\frac{1}{v _{2}} + \frac{1}{1 5} = \frac{1}{1 0}$

$v_{2} = 30 c m$

Hence, image is formed 30 cm right of the convex mirror.

From the ray diagram, it can be observed that the image is virtual.

Answer 2

Lens formula for convex lens,

\frac{1}{v} - \frac{1}{u} = \frac{1}{f}

\frac{1}{v} - \frac{1}{- 6 0} = \frac{1}{2 0}

v = 30 c m

Image (

I_{1}

) formed by the convex lens acts as an object for the convex mirror.

Since the mirror and lens are separated by 15 cm, distance between

I_{1}

and mirror is 15 cm.

i.e.

u = 15

For convex mirror,

f = \frac{R}{2} = 10 c m

From mirror equation,

\frac{1}{v _{2}} + \frac{1}{u _{2}} = \frac{1}{f _{2}}

\frac{1}{v _{2}} + \frac{1}{1 5} = \frac{1}{1 0}

v_{2} = 30 c m

Hence, image is formed 30 cm right of the convex mirror.

From the ray diagram, it can be observed that the image is virtual.