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.

By Ritesh|Updated : November 4th, 2022

A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it. The needle should be placed 50 cm from the lens and the power of lens is 4D.

Step 1: Given data

Height of image = hi

Image distance, v = 50 cm

hi = h0

Height of Object = h0

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

Step 2: To find:

Object distance (u) and lens power (P)

Step 3: Using the equation of magnification, get the object's distance u.

Magnification of a lens,

  • m = v/u
  • -1 = 50/u
  • u = -50 cm

Object is on the left side of the lens, which is a negative sign (sign convention)

Step 4: Finding the focal length using the lens formula:

Applying Lens formula

  • 1/f = 1/v - 1/u
  • 1/f = 1/50 - 1/-50
  • 1/f = 2/50
  • 1/f = 1/25
  • f = 25 cm

Step 5: Finding the power of the lens:

Power of lens P = 1/f (in meters) = 1/25 x 10-2 = 4 m-1

Diopter D is the unit used to measure a lens's power.

  • 1D = 1m-1
  • 4m-1 = 4D

Consequently, the lens's power is 4D and the object is 50 cm away from it.

Summary:

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.

At a distance of 50 cm, a convex lens creates an actual, reversed image of a needle. The lens's power is 4D, and the needle should be positioned 50 cm away from it. The focal length pf the lens is 25 cm.

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