Question

to determine the radius of curvature of a concave mirror using a spherometer. With readings

Answer 1

we know that

R = I2/6h + h/2

 

here,

R = 4 cm

h = 0.065 cm

 

now, by substituting appropriate values in above equation, we get

R = 42/(6x0.065) + 0.065/2

or

R = 41.025 + 0.0325

thus, the radius would be

R = 41.0575 cm

 

the corresponding error equation would be

ΔR/R = 2ΔI/I + Δh/h + Δh/h

 or

ΔR = + - 2R[(ΔI/I) + (Δh/h)]

 

the error in I, ΔI = least count of meter scale = 0.1 cm

the error in h, Δh = least count of spherometer = 0.001 cm

 

now, by substituting values in the above equation, we get

ΔR = + - (2x41.0575).[(0.1/4) + (0.001/0.065)]

or

ΔR = + -  82.115x[0.025 + 0.0153]

 

thus, the error in the radius would be 

ΔR = = +- 3.3 cm