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A screen is placed 90cm from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by 20cm. Determine the focal length of the lens.

By

1. Given Data

  • Distance between Object and Screen (D): 90 cm
  • Separation between lens positions (d): 20 cm

2. Formula

According to the Displacement Method principle, the focal length (f) of a convex lens is given by:

f = (D2 - d2) / 4D

3. Calculation

Step A: Calculate squares

  • D2 = 902 = 8100
  • d2 = 202 = 400

Step B: Substitute into formula

f = (8100 - 400) / (4 × 90)

f = 7700 / 360

f = 770 / 36

Step C: Final Division

f ≈ 21.39 cm

Focal Length (f) ≈ 21.39 cm
What is the Displacement Method?

This method works because of the reversibility of light paths. If an object and screen are separated by a distance D (where D > 4f), there are exactly two positions for a convex lens where a sharp image will form on the screen. The formula relates the focal length to D and the distance between these two positions (d).

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