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Question

A convex lens forms a real and inverted image of a needle at a distance of 50cm from it. Where is the needle placed in front of the convex lens if the image is equal to the size of the object? Also, find the power of the lens.


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Solution

Step 1:Given data

Image distance, v=50cm

Height of image = hi

Height of Object=ho

hi=ho

Magnification, m=-1 (image is of the same size, real and inverted)

Step 2: To find

Object distance u and power of the lens P

Step 3: Finding object distance u using the equation of magnification

Magnification of a lens,

m=vu-1=50uu=-50cm

Negative sign because the object is on the left side of the lens (sign convention )

Step 4: Using the lens formula to find the focal length

Applying Lens formula

1f=1v-1u1f=150-1-501f=2501f=125f=25cm

Step 5: Finding the power of the lens

Power of lensP=1f(inmeters)=125×10-2=4m-1

The power of a lens is measured in Diopter D

1D=1m-14m-1=4D

Therefore, the object's distance from the lens is 50cm and the power of the lens is 4D.


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