The index of refraction of a glass plate is 1.48 at `theta_(1) = 30.^@C` and varies linearly with temperature with a coefficient of `2.5 xx 10^(-5).^@C^(-1)`. At 3`0.^@C`, the length of the glass plate is 3 cm. This plate is placed in front of one of the slit n Young's double-slit experiment. If the plate is being heated so that it temperature increases at a rate of `5^(@)C^(-1)` min, the light sources has wavelength `lambda = 589 nm` and the glass plate initially ia at `theta = 30^@C`. The number of fringes that shift on the screen in each minute is nearly (use approximation)

Options

A. 1
B. 11
C. 110
D. `1.1 xx 10^(3)`

Answer

b

Explanation

Path difference `= mu - mu_(0) t_(0) = n lambda_(0)`
Where is the number of fringes that shift on the screen
`implies (mu_(0) (1 + alpha_(1) theta) t_(0) (1 + alpha_(2) theta) - mu_(0) t_(0))/(lambda_(0)) = n`
`(mu_(0) t_(0) (alpha_(1) + alpha_(2)) theta)/(lambda_(0)) = n`
Given, `mu_(0) = 1.48, t_(0) = 3 xx 10^(2) m`
`alpha_(1) = 2.5 xx 10^(-5).^@ C^(-1)`
`alpha_(2) = 0.5 xx 10^(-8).^@ C^(-1), theta = 5^(@) mim^(-1)`
`:. n = (1.48 xx 3 xx 10^(-2) (3 xx 10^(-5)) xx 5)/(589 xx 10^(-9)) = 11`