Answer:
The longest wavelength in vacuum for which there is constructive interference for the reflected light, λ = 3472.
Explanation:
Refractive index of Glass (given) = 1.5
For the case of a constructive interference,
2nt = (m + 1/2) λ
For case 1,
2nt = (m + 1/2) 496 nm
For case 2,
2nt = (m +1+ 1/2) 386 nm
2nt = (m+3/2) * 386 nm
(m + 1/2) 496 nm = (m+3/2) * 386 nm
m = 3
Inserting the value of m in 1.
2nt = (m + 1/2) 496 nm
2*1.5t = (3 + 1/2) * 496 nm
t = ((3 + 1/2) * 496 nm)/ 3
t = 578.6 nm
The thickness of the glass, t = 578.6 nm
b)
It is generally known that for constructive interference,
2nt = (m + 1/2) λ
λ = 2nt / ((m + 1/2))
For Longest Wavelength, m = 0
λ = 2*1.5*578.6/ (1/2)
λ = 3472 nm
Answer:
d = 68.5 x 10⁻⁶ m = 68.5 μm
Explanation:
The complete question is as follows:
An optical engineer needs to ensure that the bright fringes from a double-slit are 15.7 mm apart on a detector that is 1.70m from the slits. If the slits are illuminated with coherent light of wavelength 633 nm, how far apart should the slits be?
The answer can be given by using the formula derived from Young's Double Slit Experiment:

where,
d = slit separation = ?
λ = wavelength = 633 nm = 6.33 x 10⁻⁷ m
L = distance from screen (detector) = 1.7 m
y = distance between bright fringes = 15.7 mm = 0.0157 m
Therefore,

<u>d = 68.5 x 10⁻⁶ m = 68.5 μm</u>
B. they both involve wave interaction.
Answer:
-0.4 m/s
Explanation:
According to the law of conservation of momentum, the total momentum of the bullet - rifle system must be conserved.
The total momentum before the shot is zero, since they are both at rest:

While the total momentum after the shot can be written as:

where
m = 10 g = 0.010 kg is the mass of the bullet
M = 5 kg is the mass of the rifle
v = 200 m/s is the velocity of the bullet
V is the recoil velocity of the rifle
Since the total momentum is conserved, we can write:

So

And solving for V, we find the recoil velocity:

and the negative sign indicates that the velocity is opposite to the bullet.