Answer:
(a) λ = 0.496 um (b) S =2π Δ d sinθ/ λ (c) I =gI₀ (d) For the central diffraction peak, a total of 5 interference maxima are present or available.
Note: find an attached copy of a part of the solution to the given question below.
Explanation:
Solution
Recall that:
d = 6.6 um
λ₀ =d/10
λ₀ = 6.6 um
Now,
(a) We find the wavelength λ of the light in water.
Thus,
λ water = (λ₀ )/n
= 0.66/1.33
So,
λ water = λ = 0.496 um
(b) We find the phase difference between the waves from slit 1 and 2
Now,
if a <<d and a<<λ
Then the path difference between the rays will be
Δ S₂N = Δ d sinθ
Thus, the phase difference becomes,
S = 2π Δ/λ is S= 2π Δ d sinθ/ λ
<u>(</u>c) The next step is to derive an expression for the intensity I as function of O and other relevant parameters.
Now,
Let p be the point where these two rays interfere with each other.
Thus,
The electric field vector coming out from slot and and slot 2 is
E₁= E₀₁ cos (ks₁ p - wt) i
E₂ = E₀₂ cos (ks₂ p - wt) i
Note: Kindly find an attached copy of a part of the solution to the given question below.
Answer:
a) n2 = 1.55
b) 408.25 nm
c) 4.74*10^14 Hz
d) 1.93*10^8 m/s
Explanation:
a) To find the index of refraction of the syrup solution you use the Snell's law:
(1)
n1: index of refraction of air
n2: index of syrup solution
angle1: incidence angle
angle2: refraction angle
You replace the values of the parameter in (1) and calculate n2:

b) To fond the wavelength in the solution you use:

c) The frequency of the wave in the solution is:

d) The speed in the solution is given by:

That's "displacement". It only depends on the beginning and ending locations, and doesn't care about the route between them.
The amount of heat given by the water to the block of ice can be calculated by using

where

is the mass of the water

is the specific heat capacity of water

is the variation of temperature of the water.
Using these numbers, we find

This is the amount of heat released by the water, but this is exactly equal to the amount of heat absorbed by the ice, used to melt it into water according to the formula:

where

is the mass of the ice while

is the specific latent heat of fusion of the ice.
Re-arranging this formula and using the heat Q that we found previously, we can calculate the mass of the ice:
To develop this problem, it is necessary to apply the concepts related to the description of the movement through the kinematic trajectory equations, which include displacement, velocity and acceleration.
The trajectory equation from the motion kinematic equations is given by

Where,
a = acceleration
t = time
= Initial velocity
= initial position
In addition to this we know that speed, speed is the change of position in relation to time. So

x = Displacement
t = time
With the data we have we can find the time as well




With the equation of motion and considering that we have no initial position, that the initial velocity is also zero then and that the acceleration is gravity,





Therefore the vertical distance that the ball drops as it moves from the pitcher to the catcher is 1.46m.