For a glass prism of refracting, angle `60^@,` the minimum angle of deviation, `D_m` is fonud to be `36^@` with a maximum error of `1.05^@,` when a beam of parallel light is insident on the prism. Find the range of experimental value of refactive index `mu.` it is known that refractive index `mu` of material of prism is given by `mu =(sin(A+D_m)/(2))/(sinA//2)`

Explanation

`Here, A = 60^@, D_m = (36^@+-1.05^@),mu = ?`
Taking `(D_m) = 36^@ 1.05^@ = 37.05^@`,
`mu_1 = sin(A+D_1)/((2)/(sin A//2)) = (sin(60+37.05)^@//2)/(sin 60^@//2) = (sin69.52^@)/(sin30^@) = (0.7492)/(1//2)`
`=1.4984 = 1.50("rouding off to two decimal places")`
Taking`(D_m)_2 = 36^@ -1.05^@ = 34.95^@`,
`mu_2 = (sin(A+D_m)_2)/(2)/(sinA//2) = (sin(60+34.95)^@//20)/(sin60^@//2) = (sin47.48^@)/(sin30^@) = (0.7370)/(1//2) = 1.4740`
`=1.47("rounding off to two decimal places")`
Hence, `1.47_mu1.50`with a mean value of 1.49