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A point object O is placed on the principal axis of a convex lens of focal length f=20cm at a distance of 40cm to the left of it. The diameter of the lens is 10cm. An eye is placed 60cm to right of the lens and a distance h below the principal axis. The maximum value of h to see the image is____.


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Solution

Step 1. Given data

Focal length f=20cm

Distance =40cm

We have to find the maximum value of distance h.

Step 2. Formula used.

A lens is a piece of a refracting medium bounded by two surfaces, at least one of which is a curved surface.

We will calculate the image distance by using the lens formula.

This formula represents the relation between object distance u, image distance v, and focal length f.

1f=1v-1u

Here,

f=20cm

According to the sign of convention, object distance u=-40cm

v=?

Step 3. Calculate the image distance.

By using the lens formula, we get,

120=1v-1-40

120=1v+140

1v=120-140

1v=140

v=40cm

So, the image distance is 40cm, which means the image is formed at the center of curvature.

Draw the ray diagram

Step 4. Find the value of distance.

According to the above figure, CED and CAB are in symmetric form.

So,

ABDE=BCDC

5h=4020

5h=2

h=52

h=2.5cm

The maximum value of h to see the image is 2.5cm.


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