Question

1) Separation between 2 slits is 0.450 mm produces fringes on the screen located 2.80 m away when a red light of He-Ne laser with the wavelength of 680 nm falls on the slits. Determine the distance between the first and third bright fringes on the screen. 2) To minimize reflection of normally incident green light of 550 nm, the glass of a camera lens is covered by a coating of 115 nm thickness. Knowing that the index of refraction of coating is less than the index of refraction of the glass, determine the index of refraction of the coating. See formulas sheet for the index of refraction for glass.

Answer 1

The distance between the first and third bright fringes on the screen is 0.0105 m.

Step-by-step explanation:

The distance between the first and third bright fringes can be determined using the formula:

y = m * λ * L / d

Where:

• y is the distance between fringes
• m is the order of the fringe (in this case, m = 3)
• λ is the wavelength of the light
• L is the distance between the slits and the screen
• d is the separation between the slits

Substituting the values:

`y = 3 * (680 * 10^(-9)) * 2.80 / (0.450 * 10^(-3))`

Solving the equation gives:

y = 0.0105 m

Answer 2

The distance between the first and third bright fringes on the screen is 8.44 x 10^-3 meters and the index of refraction of the coating is 4.78.

1) To determine the distance between the first and third bright fringes on the screen, we need to first calculate the distance between adjacent fringes using the formula:

Δy = (λ * L) / d

where Δy is the distance between adjacent fringes, λ is the wavelength of the light, L is the distance between the slits and the screen, and d is the separation between the slits.

Given:

λ = 680 nm = 680 x 10^-9 m

L = 2.80 m

d = 0.450 mm = 0.450 x 10^-3 m

Plugging these values into the formula, we get:

Δy = (680 x 10^-9 m * 2.80 m) / (0.450 x 10^-3 m)

= 4.22 x 10^-3 m

The distance between the first and third bright fringes will be twice the distance between adjacent fringes. So,

Distance between the first and third bright fringes = 2 * Δy

= 2 * 4.22 x 10^-3 m

= 8.44 x 10^-3 m

Therefore, the distance between the first and third bright fringes on the screen is 8.44 x 10^-3 meters.

2) To determine the index of refraction of the coating, we can use the formula:

n = λ / t

where n is the index of refraction, λ is the wavelength of the light, and t is the thickness of the coating.

Given:

λ = 550 nm = 550 x 10^-9 m

t = 115 nm = 115 x 10^-9 m

Plugging these values into the formula, we get:

n = (550 x 10^-9 m) / (115 x 10^-9 m)

= 4.78

Therefore, the index of refraction of the coating is 4.78.