A needle 4cm high is placed in front of a lens. Image of the needle is real, inverted nd 6 cm high, when the distance between the needle and its image is 20 cm. Find the focal length of lens.?

Question

Answer

Problem:

A needle 4cm high is placed in front of a lens. Image of the needle is real, inverted nd 6 cm high, when the distance between the needle and its image is 20 cm. Find the focal length of lens?

Solution:

Given:

Height of needle, h = 4 cm

Height of image, h' = -6 cm (negative sign indicates that the image is inverted)

Distance between the needle and its image, d = -20 cm (negative sign indicates that the image is formed on the opposite side of the lens)

We need to find the focal length of the lens, f.

Using the Lens Formula:

The lens formula is:

1/f = 1/v - 1/u

f is the focal length of the lens

u is the distance of the object from the lens

v is the distance of the image from the lens

Since the image is real and inverted, the distance of the image from the lens (v) is negative. Using the sign convention:

u = -20 cm

v = -d = 20 cm

h = 4 cm

h' = -6 cm

Substituting the values in the lens formula:

1/f = 1/20 + 1/-20

1/f = 0

This is not possible as the focal length cannot be zero. Hence, the given values are not possible and there may be some error in measurement or calculation.

Conclusion:

The given values do not result in a valid solution for the focal length of the lens. It is recommended to recheck the measurements and calculations.

Answer

magnification is image distance / object distance = image height/object height = 1.5.

As this lens is able to get an inverted image it is a convex lens, because a concave lens can only form virtual images.

let object height be u and image height be v. so v/u = 1.5.

v + u = 20 and v = 1.5 u ,

combining these we get 1.5u + u = 20 , therefore 2.5u = 20 , and u = 8. also v must be 12

according to formula

1/u + 1/v = 1/f

1/8 + 1/12 = 1/f

20/96 = 1/f

so f = 96/20 = 4.8 cm convex lens

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