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.

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

Calculations:

1. μ-v graph:

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


2. 1/μ and 1/v graph:

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

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.