Two identical spherical balls, each of mass m, are placed as shown in figure. Plot the variation of g(gravitation intensity) along the x-axis due to both the masses.

Explanation

In the minimum deviation position, `r = (A)/(2) = (60^(@))/(2)` for both the prisms. Since `A = 60^(@)` for both the prisms. For the first prism, `mu_(1) = 1.50` and `sin i_(1) = mu, sin r_(1) = 1.50, sin 30^(@) = 0.75`

`:. i_(1) = 48^(@)35'`
For the second prism, `mu_(2) = 1.68` and `sin i_(1) = mu_(2)sin r_(1)' = 1.68 sin 30^(@) = 0.84`
`i'_(1) = 57^(@)9'`
Let the angle between the bases of the prism be `alpha`.
`alpha = 360^(@) - (60^(@) + beta + 60^(@))`
But `beta + 90^(@) - i_(1) + 90^(@) - i_(1) = 180^(@)`
`beta = i_(1) + i'_(1) = 48^(@)35^(@) + 57^(@)9' = 105^(@)44'`
`:. alpha = 360^(@) - (120^(@) + 105^(@)44') = 134^(@)16'`
(ii) In the minimum deviation position, `i = (A+delta)/(2)`
`delta = 2i - A`
For the first prism, `delta_(1) = 2i_(1) - A = 2(48^(@)35') - 60^(@) = 37^(@)10'`
For the second prism, `delta_(2) = 2i_(1) - A = 2(57^(@)9') - 60^(@) = 54^(@)18'`