Optics Chapter on Diffraction and Interference

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Questions and Answers

What is the condition for minima in Newton's rings experiment?

Δ = (n + 2)λ (correct)

Δ = (n + 1)λ

2μt = (2n + 1)λ

2μt = nλ

When does constructive interference occur in Newton's rings?

When Δ = 2μt + 2

When Δ = n/2 λ

When Δ = (n + 1)λ

When Δ = nλ (correct)

Which equation represents the condition for maxima in the Newton's rings experiment?

2μt = nλ

2μt = (2n - 1)λ (correct)

Δ = 2nλ

Δ = n/2 λ

According to the properties of circles, what does the product of intercepts equal?

The product of sections of the diameter Signup and view all the answers

What is the relationship between the radius of a ring and the thickness of the air film in Newton's rings?

Radius is directly proportional to thickness Signup and view all the answers

What is the relationship between the number of lines per cm of a grating and its resolving power?

More lines per cm increases resolving power. Signup and view all the answers

What phenomenon causes the formation of alternating dark and bright fringes in Newton's Rings?

Interference between reflected waves from two surfaces. Signup and view all the answers

In the Newton's Ring arrangement, what happens to the thickness of the air film?

It gradually increases as one moves away from the point of contact. Signup and view all the answers

How are the fringes observed when monochromatic light is used in a Newton's Ring experiment?

They appear as alternating dark and bright concentric rings. Signup and view all the answers

What is the primary effect of increasing the thickness of the air film in Newton's Rings?

It changes the pattern of the interference fringes. Signup and view all the answers

In the Newton's Rings experiment using white light, what kind of fringes are formed?

Colored fringes. Signup and view all the answers

What is the role of the plano-convex lens in the formation of Newton's Rings?

It creates an air film with varying thickness. Signup and view all the answers

What is a necessary condition for the formation of the interference patterns in the Newton's Rings experiment?

The rays must be coherent. Signup and view all the answers

What is the formula for the path difference between the two reflected rays in a wedge-shaped film?

Δ = μ(BC + CI) - BE Signup and view all the answers

In the right angled triangle ΔBED, what does the equation sin i = BE/BD represent?

The relationship between angle i and the side BD Signup and view all the answers

What is the significance of equation (5), BE = μBC?

It relates the path lengths in the film and air. Signup and view all the answers

What does equation (6) indicate about the path difference Δ?

Δ is dependent on the refractive index and thickness. Signup and view all the answers

How is CI expressed in equation (7)?

CI = 2t cos(r + θ) Signup and view all the answers

What does equation (8) derive for the path difference in a wedge-shaped film?

Δ = 2μt cos(r + θ) Signup and view all the answers

What condition is implied when light reflects off the top surface of an air film?

There is no phase change. Signup and view all the answers

Which triangle is used to establish the relationship sin r in equation (4)?

Triangle ΔBCD Signup and view all the answers

What does the variable μ represent in the context of the given equations?

The refractive index Signup and view all the answers

How is the distance CI derived in the wedge-shaped film scenario?

CI = DI cos(r + θ) Signup and view all the answers

What does the equation $𝐷𝐵 × 𝐵𝐸 = 𝐴𝐵 × 𝐵𝐶$ represent in the context of a plano convex lens?

The geometric relationship of segments in the lens. Signup and view all the answers

From the equations given, what simplification is made for $t^2$?

It is considered negligible. Signup and view all the answers

What does the final equation $t = \frac{r^2}{2R}$ indicate about $t$?

t is directly proportional to the square of the radius. Signup and view all the answers

In the condition for maxima $2 u t = (2n - 1)\lambda$, what does $n$ represent?

The order of the maximum. Signup and view all the answers

What is the significance of the equation $r^2 = 2Rt$?

It defines the curvature of the lens. Signup and view all the answers

What is the relationship between the diameter of the nth bright ring and the wavelength in air when the refractive index is 1?

Diameter is directly proportional to the wavelength. Signup and view all the answers

Using equation (10), what does the diameter D depend on for the nth bright ring?

Wavelength, R, and the refractive index. Signup and view all the answers

For which values of n does the nth bright ring occur?

The odd integers. Signup and view all the answers

How is the diameter D of the bright rings related to the term (2n - 1)?

D is proportional to (2n - 1). Signup and view all the answers

What condition indicates the formation of dark rings?

2𝜇𝑡 = n𝜆 Signup and view all the answers

What did the simplification in equation (10) reveal about the dependency of D?

D is influenced by the odd natural number n. Signup and view all the answers

If the refractive index 𝜇 changes, how does it affect the diameter D according to equation (10)?

D decreases as 𝜇 increases. Signup and view all the answers

What does the expression D ∝ (2n - 1) indicate about the pattern of the bright rings?

The diameter of the bright rings increases with an odd integer sequence. Signup and view all the answers

Study Notes

Resolving Power of a Plane Diffraction Grating

The resolving power of a plane diffraction grating is given by dλ = nN/λ, where n is the order of the spectrum and N is the total number of lines on the grating.
Increasing the number of lines per centimeter increases the resolving power.

Newton's Rings

Newton's rings are a phenomenon of interference observed when a plano-convex lens is placed on a glass plate, creating an air film of varying thickness.
Monochromatic light incident on the film produces concentric circular bright and dark fringes due to interference between reflections from the top and bottom surfaces of the air film.
White light produces colored fringes.
The thickness of the air film is zero at the point of contact and increases radially outwards.

Interference in a Wedge-Shaped Film

Path difference (Δ) between two reflected rays in the air film is given by Δ = 2μt cos(r + θ), where μ is the refractive index of the film (air, in this case), t is the film thickness, r is the angle of refraction, and θ is the angle of incidence on the lower surface.
There is no phase change upon reflection from the top surface (rare medium to denser medium).

Conditions for Maxima and Minima in Newton's Rings

Condition for minimum intensity (dark rings): 2μt = nλ where n = 0, 1, 2, 3... The center is generally dark.
Condition for maximum intensity (bright rings): 2μt = (2n - 1)λ/2 where n = 1, 2, 3...

Diameter of Newton's Rings

Bright rings: The radius (r_n) of the nth bright ring is given by rn2 = (2n - 1)λR/(2μ), where R is the radius of curvature of the plano-convex lens. The diameter (D_n) is then Dn = √[2(2n - 1)λR/μ]. For air (μ=1), Dn = √[2(2n-1)λR]. Diameter is proportional to √(2n-1).
Dark rings: The condition for dark rings is 2μt = nλ (n = 1,2,3...). The derivation for diameter is not provided in the given text.

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Description

Explore the concepts of resolving power of plane diffraction gratings, Newton's rings, and interference in wedge-shaped films. This quiz tests your understanding of the principles behind these optical phenomena and their mathematical descriptions. Enhance your knowledge with this focused quiz on optics.