Q63 / 90 · JEE Main 2023 (06 Apr Shift 2) · Physics

A 2 meter long scale with least count of 0.2 cm is used to measure the locations of objects on an optical bench. While measuring the focal length of a convex lens, the object pin and the convex lens are placed at 80 cm mark and 1 m mark, respectively. The image of the object pin on the other side of lens coincides with image pin that is kept at 180 cm mark. The % error in the estimation of focal length is:

  • A
    0.85
  • Correct answer
    B
    1.70
  • C
    1.02
  • D
    0.51

Solution

The formula for a lens is given by 1f=1v-1u   ...(i)

u=100±0.2 cm-80±0.2 cm=20±0.4 cm

v=180±0.2 cm-100±0.2 cm=80±0.4 cm

Substituting the values in the equation of focal length,

1f=1v-1u=180--120=580

⇒f=16 cm

Differentiating the equation (i)

dff2=dvv2+duu2(Only positive sign is considered for error calculation)

=0.46400+0.4400=0.4×176400

⇒df=0.4×176400×162=0.272

The percentage error is 

dff×100=0.27216×100=1.70%

Hence, the correct answer is option: 'B'.

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