Question 48: Units , Dimensions and Error Analysis

Question

For the determination of refractive index of glass slab, a travelling microscope is used whose main scale contains 300 equal divisions equals to 15 cm . The vernier scale attached to the microscope has 25 divisions equals to 24 divisions of main scale. The least count (LC) of the travelling microscope is (in cm ) :

Accepted Answer

Determine one main scale division (msd):
$    300 \, 	ext{msd} = 15 \, 	ext{cm}    $
Therefore,
$    1 \, 	ext{msd} = \frac{15}{300} \, 	ext{cm} = 0.05 \, 	ext{cm}    $
Determine one vernier scale division (vsd):
$    25 \, 	ext{vsd} = 24 \, 	ext{msd}    $
Therefore,
$    1 \, 	ext{vsd} = \frac{24}{25} \, 	ext{msd}    $
Calculate the least count (LC):
The least count is given by the difference between one main scale division and one vernier scale division:
$    	ext{LC} = 1 \, 	ext{msd} - 1 \, 	ext{vsd}    $
Substitute the expression for 1 vsd:
$    	ext{LC} = 1 \, 	ext{msd} - \frac{24}{25} 	imes 1 \, 	ext{msd}    $
This simplifies to:
$    	ext{LC} = \frac{1}{25} 	imes 1 \, 	ext{msd}    $
Calculate the LC in cm:
Substituting the value of 1 msd:
$    	ext{LC} = \frac{1}{25} 	imes 0.05 \, 	ext{cm} = 0.002 \, 	ext{cm}    $
Hence, the least count of the traveling microscope is 0.002 cm.

Answer

0.002

Answer

0.0025

Answer

0.0005

Answer

0.001

Units , Dimensions and Error Analysis

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