Question

An object is placed at a distance of 20 cm from a concave lens of focal length
15 cm. Find the distance of the image from the lens and draw its ray diagram.

Answer 1

-8.57 cm is the required answer.

GIVEN:

• Object distance, u = - 20 cm
• The given lens is concave lens.
• Focal length of concave lens , f = -15 cm

TO FIND:

Distance of image, v

FORMULA:

According to lens formula,

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

SOLUTION:

$\frac{1}{f} = \frac{1}{v} - \frac{1}{u} \\ \\ \frac{1}{ - 15} = \frac{1}{v} - \frac{1}{ - 20} \\ \\ - \frac{1}{15} = \frac{1}{v} + \frac{1}{20} \\ \\ - \frac{1}{15} - \frac{1}{20} = \frac{1}{v} \\ \\ \frac{1}{v} = \frac{ - 20 - 15}{15 \times 20} \\ \\ \frac{1}{v} = \frac{ - 35}{15 \times 20} \\ \\ v = - \frac{15 \times 20}{35} \\ \\ v = - \frac{ 3 \times20 }{7} \\ \\ v = - \frac{60}{7} \\ \\ v = - 8.57 \: cm$

ANSWER:

Distance of the image is -8.57 cm.

Negative sign indicates that the image is formed to the left of the concave lens.

RAY DIAGRAM:

For the ray diagram, refer to the attachment.

POINTS TO NOTICE:

• Focal length of concave lens is negative and convex lens is positive.

• Concave lens is a diverging lens and convex lens is a converging lens.

• Ray passing parallel to axis pass through focus after reflection.

• Ray passing through the optic axis goes undeviated after reflection.