Answer:
a ) 1.267 radian
b ) 1.084 10⁻³ mm
Explanation:
Distance of screen D = 1.65 m
Width of slit d = ?
Wave length of light λ = 687 nm.
Distance of second minimum fro centre y = 2.09 cm
Angle of diffraction = y / D
= 2.09 /1.65
= 1.267. radian
Angle of diffraction of second minimum
= 2 λ / d
so 2 λ / d = 1.267
d = 2 λ / 1.267 = (2 x 687 ) /1.267 nm
=1084.45 nm = 1.084 x 10⁻³ mm.
A) 4.7 cm
The formula for the angular spread of the nth-maximum from the central bright fringe for a diffraction from two slits is

where
n is the order of the maximum
is the wavelength
is the distance between the slits
In this problem,
n = 5


So we find

And given the distance of the screen from the slits,

The distance of the 5th bright fringe from the central bright fringe will be given by

B) 8.1 cm
The formula to find the nth-minimum (dark fringe) in a diffraction pattern from double slit is a bit differente from the previous one:

To find the angle corresponding to the 8th dark fringe, we substitute n=8:

And the distance of the 8th dark fringe from the central bright fringe will be given by

Gold’s molar mass is about 196 while aluminum is about 27, thus 50cm of gold has more mass
Answer:
dT(t)/dt = k[T5 - T(t)]
Explanation:
Since T(t) represents the temperature of the object and T5 represents the temperature of the surroundings, according to Newton's law of cooling, the rate at which an object's temperature changes is directly proportional to the difference in temperature between the object and the surrounding medium, that is dT(t)/dt ∝ T5 - T(t)
Introducing the constant of proportionality
dT(t)/dt = k[T5 - T(t)]
which is the desired differential equation