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The radius of a concave mirror ...

The radius of a concave mirror measured by spherometer is given by ` R = (( l^ 2 ) /( 6 h ) + ( h ) /(2)) `
The values of 'l' and 'h' are 4 cm and 0.065 cm respectively. Compute the error measurement of radius of curvature.

Text Solution

Verified by Experts

Least count of spherometer is 0.001 cm and error in 'l' and 'h' is ` pm 0.001 ` km i.e., ` Delta l and Delta h= pm 0.001 cm `
` ( Delta R ) /( R) = (( 2 Delta l)/(l) + ( 6 Delta h ) /(h) + (1 ) /(2) (Delta h) /(h)) = ( 2 xx 0.001 ) /(4) + (6 xx 0.001 ) /(0.065 ) + ( 0.001)/(2 xx 0.065 ) `
` therefore ( Delta R ) /( R) = 0.10049 `
i.e., ` Delta R = 0.10049 R = 0.10049 xx 41.058 = 4.1259 cm `
Where ` R = ( 4 ^ 2 ) /( 6 xx 0.065 ) + ( 0.065 ) /2 = 41. 0256 + 0.0325 = 41.058 ` cm
Hence ` R = ( 41.058 pm 4.123 ) cm `
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