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Home Physics Class 12 Physics To find the value of ‘v’ for different values of ‘u’ in case of a concave mirror & to find its focal length
Class 12 Physics Lab Experiments

To find the value of ‘v’ for different values of ‘u’ in case of a concave mirror & to find its focal length



Aim

To find the value of v for different values of ‘u’ in case of a concave mirror & to find its focal length.

Apparatus

An optical bench with three uprights. Concave mirror, a mirror holder, two optical needles, a knitting needle & a half – meter scale.

Formulae Used:

The mirror formula is: The mirror formula is: 1/ƒ = 1/μ+1/μ

We have, ƒ = μv /μ + v

Required shunt resistant S is made using a uniform wire whose, specific resistance is σ (known) & its length:

Where, ƒ = focal length of concave mirror.

μ= distance of object needle from pole of mirror.

v = distance of image needle from pole of mirror.

Ray Diagram

Observation:

Rough focal length of given concave mirror = 10.9 cm

Actual length of the knitting needle, x = 15 cm

Observed distance between the mirror & object needle when knitting needle is placed between them, y = 15.2 cm.

Observed distance between the mirror & image needle when knitting needle is placed between them, z = 15.8 cm.

Index error for μ,e1= y - x = -0.2 cm

Index error for v, e2= z - x = -0.8 cm

S.No. Position/Concave Mirror P (cm)/Object Needle O/Image Needle I Corrected Distance/PO μcm/PI v cm 1/μ(cm -1) 1/v (cm-1)
1 0.0 18 26 17.8 25.2 0.056 0.037
2 0.0 17 30.3 16.8 29.5 0.06 0.034
3 0.0 16 33.4 15.8 32.6 0.063 0.031
4 0.0 26 18 25.8 17.2 0.038 0.058
5 0.0 30.3 17 30.1 16.2 0.033 0.061
5 0.0 30.4 16 33.2 15.2 0.030 0.065

Calculations:

  1. μ-v graph:
  2. As μ= v, 1/ƒ=2/μ or 2/1/μ or 2/v and ƒ=μ/2 or v/2

    Hence,ƒ=-OD/2 = -21/2 = -10.5 cm

    Graph Scale: X’ axis: 1 cm = 5 cm of μ

    Y’ axis: 1 cm = 5 cm of v

    Also ƒ=-OB/2 = -10.5 cm

    Mean value of ƒ = -10.5 cm =-OB/2 = -10.5 cm

    Graph between u&v
  3. 1/μ and 1/v graph:
  4. The focal length, ƒ = -1/OA = -1/OB = -10.47 cm

    Graph Scale: X’ axis: 1 cm = 0.01 cm -1oƒ1/v

    Graph Scale: Y’ axis: 1 cm = 0.01 cm -1oƒ1/v

    Graph between 1_u and 1_v

Result:

The focal length of the given concave mirror:

From μ – v graph is : ƒ = –10.5 cm

1/μ – 1/v graph is : ƒ = –10.47 cm

Precautions:

  1. The uprights should be vertical.
  2. Tip-to-tip parallax should be removed between the needle I and image of needle O.
  3. To locate the position of the image the eye should be at least 30 cm away from the needle.

Sources of Error:* The uprights may not be vertical. * Parallax removal may not be perfect.