To find the value of v for different values of ‘u’ in case of a concave mirror & to find its focal length.
An optical bench with three uprights. Concave mirror, a mirror holder, two optical needles, a knitting needle & a half – meter scale.
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.
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,e_{1}= y - x = -0.2 cm
Index error for v, e_{2}= 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 |
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
The focal length, ƒ = -1/OA = -1/OB = -10.47 cm
Graph Scale: X’ axis: 1 cm = 0.01 cm ^{-1}oƒ1/v
Graph Scale: Y’ axis: 1 cm = 0.01 cm ^{-1}oƒ1/v
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
Sources of Error:* The uprights may not be vertical. * Parallax removal may not be perfect.
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