Question

the radius of curvature of concave mirror measured by a spherometer is given by - R=I2/6h+h/2. the value of i and h are 4cm and 0.065 cm respectively. compute the error in measurement of radius of curvature.

Answer 1

the radius of curvature of concave mirror measured by a spherometer is given by - R=I2/6h+h/2. the value of i and h are 4cm and 0.065 cm respectively. compute the error in measurement of radius of curvature it may 0.5

Answer 2

Answer:

The error in the radius would be $\Delta R=3.31$

Explanation:

Given that,

The value of l = 4 cm

The value of h = 0.065 cm

The radius of curvature of concave mirror

$R=\dfrac{l^2}{6h}+\dfrac{h}{2}$.....(I)

Put the value of i and h in the equation (I)

$R=\dfrac{4^2}{6\times0.065}+\dfrac{0.065}{2}$

$R=41.05\ cm$

The corresponding error equation would be

$\dfrac{\Delta R}{R}=\dfrac{2\Delta l}{l}+\dfrac{\Delta h}{h}+\dfrac{\Delta h}{h}$

We know that,

The least count of meter scale = 0.1 cm

The least count of spherometer =0.001 cm

Now, we substitute the value in the above equation

$\Delta R=R\times(\dfrac{2\Delta l}{l}+\dfrac{\Delta h}{h}+\dfrac{\Delta h}{h})$

$\Delta R=41.05(\dfrac{2\times0.1}{4}+\dfrac{0.001}{0.065}+\dfrac{0.001}{0.065})$

$\Delta R=3.31$

Hence, The error in the radius would be $\Delta R=3.31$