Convex Lens Focal Length, Galvanometer Resistance & Wire Resistance

Posted on Feb 14, 2025 in Physics

Aim: Convex Lens Focal Length

To find the focal length of a convex lens by plotting a graph:

  • Between u and v
  • Between 1/v and 1/u

Apparatus

An optical bench with three uprights, a convex lens, lens holder, two optical needles, a knitting needle, and a half-meter scale.

Formula Used

The relation between u, v, and f for a convex lens is: 1/f = 1/v – 1/u

Where:

  • f: focal length of the convex lens
  • u: distance of the object needle from the lens’ optical center
  • v: distance of the image needle from the lens’ optical center

Observations

  1. Rough focal length of the lens = 10 cm
  2. Actual length of knitting needle, x = 15 cm
  3. Observed distance between object needle & the lens when the knitting needle is placed between them, y = 15.2 cm
  4. Observed distance between image needle & the lens when the knitting needle is placed between them, z = 14.1 cm
  5. Index correction for the object distance u, x – y = – 0.2 cm
  6. Index correction for the image distance v, x – z = +0.9 cm

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Calculation of Focal Length by Graphical Method

  1. u – v graph: The graph is a rectangular hyperbola:

    Scale: X’ axis: 1 cm = 5 cm of u; Y’ axis: 1 cm = 5 cm of v

    AB = AC = 2f or OC = OB = 2

    f = OB/2 and also f = OC/2

    Mean value of f = 10.1 cm.

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Formulae Used

  1. The resistance of the given galvanometer as found by the half-deflection method: G = R S/R – S

Where:

  • R: resistance connected in series with the galvanometer
  • S: shunt resistance
  1. Figure of merit: k = E/(R+G)θ

    Where:

    • E : emf of the cell
    • θ : deflection produced with resistance R.

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Mean R = 1.56

Length of resistance wire: 28 cm

Graph between Potential Difference & Current

Scale: X – axis : 1 cm = 0.1 V of potential difference; Y – axis: 1 cm = 0.1 A of current

The graph comes out to be a straight line.

Result

It is found that the ratio V/I is constant, hence the current-voltage relationship is established i.e., V proportional to I or Ohm’s Law is verified.

Unknown resistance per cm of given wire = 5.57 x 10-2 ohm cm-1

Precautions

  • Voltmeter and ammeter should be of proper range.
  • The connections should be neat, clean & tight.

Source of Error

  • The rheostat may have high resistance.
  • The instrument screws may be loose.