Question 2 Page 184 - Chapter 10 Class 10 - Light - Reflection and Refraction

Last updated at Sept. 10, 2019 by Teachoo

A convex lens forms a real and inverted image of a needle at a distance of 50 cm 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

Question 2 Page 184
A convex lens forms a real and inverted image of a needle at a distance of 50 cm 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
Given that
Image formed is real and of same size,
Hence, Magnification = −1
Since Image formed is real,
∴ Image distance is positive
Image distance = v = + 50 cm
Let the object distance = u
We know that,
Magnification in a lens = 𝑣/𝑢
−1 = 50/𝑢
∴ u = 50/(−1)
u = − 50 cm
∴ Needle is placed 50 cm infront of the lens
Now,
In a convex lens
Size of image is same as the size of object
∴ Object must be placed at Twice the Focal Length
Thus,
Object distance = 2 × Focal length
50 = 2 × Focal length
Now,
In a convex lens
Size of image is same as the size of object
∴ Object must be placed at Twice the Focal Length
Thus,
Object distance = 2 × Focal length
50 = 2 × Focal length
Focal length = 50/2
Focal length = 25 cm
Focal length = (25 )/100 m
Focal length = 0.25 m
Now,
Power of a lens = 1/(𝐹𝑜𝑐𝑎𝑙 𝐿𝑒𝑛𝑔𝑡ℎ)
= 1/0.25
= 100/25
= 4 D
∴ Power of the lens is 4 D

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