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Questions and Answers
What is the condition for minima in Newton's rings experiment?
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 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?
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?
According to the properties of circles, what does the product of intercepts equal?
What is the relationship between the radius of a ring and the thickness of the air film in Newton's rings?
What is the relationship between the radius of a ring and the thickness of the air film in Newton's rings?
What is the relationship between the number of lines per cm of a grating and its resolving power?
What is the relationship between the number of lines per cm of a grating and its resolving power?
What phenomenon causes the formation of alternating dark and bright fringes in Newton's Rings?
What phenomenon causes the formation of alternating dark and bright fringes in Newton's Rings?
In the Newton's Ring arrangement, what happens to the thickness of the air film?
In the Newton's Ring arrangement, what happens to the thickness of the air film?
How are the fringes observed when monochromatic light is used in a Newton's Ring experiment?
How are the fringes observed when monochromatic light is used in a Newton's Ring experiment?
What is the primary effect of increasing the thickness of the air film in Newton's Rings?
What is the primary effect of increasing the thickness of the air film in Newton's Rings?
In the Newton's Rings experiment using white light, what kind of fringes are formed?
In the Newton's Rings experiment using white light, what kind of fringes are formed?
What is the role of the plano-convex lens in the formation of Newton's Rings?
What is the role of the plano-convex lens in the formation of Newton's Rings?
What is a necessary condition for the formation of the interference patterns in the Newton's Rings experiment?
What is a necessary condition for the formation of the interference patterns in the Newton's Rings experiment?
What is the formula for the path difference between the two reflected rays in a wedge-shaped film?
What is the formula for the path difference between the two reflected rays in a wedge-shaped film?
In the right angled triangle ΔBED, what does the equation sin i = BE/BD represent?
In the right angled triangle ΔBED, what does the equation sin i = BE/BD represent?
What is the significance of equation (5), BE = μBC?
What is the significance of equation (5), BE = μBC?
What does equation (6) indicate about the path difference Δ?
What does equation (6) indicate about the path difference Δ?
How is CI expressed in equation (7)?
How is CI expressed in equation (7)?
What does equation (8) derive for the path difference in a wedge-shaped film?
What does equation (8) derive for the path difference in a wedge-shaped film?
What condition is implied when light reflects off the top surface of an air film?
What condition is implied when light reflects off the top surface of an air film?
Which triangle is used to establish the relationship sin r in equation (4)?
Which triangle is used to establish the relationship sin r in equation (4)?
What does the variable μ represent in the context of the given equations?
What does the variable μ represent in the context of the given equations?
How is the distance CI derived in the wedge-shaped film scenario?
How is the distance CI derived in the wedge-shaped film scenario?
What does the equation $𝐷𝐵 × 𝐵𝐸 = 𝐴𝐵 × 𝐵𝐶$ represent in the context of a plano convex lens?
What does the equation $𝐷𝐵 × 𝐵𝐸 = 𝐴𝐵 × 𝐵𝐶$ represent in the context of a plano convex lens?
From the equations given, what simplification is made for $t^2$?
From the equations given, what simplification is made for $t^2$?
What does the final equation $t = \frac{r^2}{2R}$ indicate about $t$?
What does the final equation $t = \frac{r^2}{2R}$ indicate about $t$?
In the condition for maxima $2
u t = (2n - 1)\lambda$, what does $n$ represent?
In the condition for maxima $2 u t = (2n - 1)\lambda$, what does $n$ represent?
What is the significance of the equation $r^2 = 2Rt$?
What is the significance of the equation $r^2 = 2Rt$?
What is the relationship between the diameter of the nth bright ring and the wavelength in air when the refractive index is 1?
What is the relationship between the diameter of the nth bright ring and the wavelength in air when the refractive index is 1?
Using equation (10), what does the diameter D depend on for the nth bright ring?
Using equation (10), what does the diameter D depend on for the nth bright ring?
For which values of n does the nth bright ring occur?
For which values of n does the nth bright ring occur?
How is the diameter D of the bright rings related to the term (2n - 1)?
How is the diameter D of the bright rings related to the term (2n - 1)?
What condition indicates the formation of dark rings?
What condition indicates the formation of dark rings?
What did the simplification in equation (10) reveal about the dependency of D?
What did the simplification in equation (10) reveal about the dependency of D?
If the refractive index 𝜇 changes, how does it affect the diameter D according to equation (10)?
If the refractive index 𝜇 changes, how does it affect the diameter D according to equation (10)?
What does the expression D ∝ (2n - 1) indicate about the pattern of the bright rings?
What does the expression D ∝ (2n - 1) indicate about the pattern of the bright rings?
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Study Notes
Resolving Power of a Plane Diffraction Grating
- The resolving power of a plane diffraction grating is given by
dλ = nN/λ, wherenis the order of the spectrum andNis 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), whereμis the refractive index of the film (air, in this case),tis the film thickness,ris the angle of refraction, andθis 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 = nλwheren = 0, 1, 2, 3...The center is generally dark. - Condition for maximum intensity (bright rings):
2μt = (2n - 1)λ/2wheren = 1, 2, 3...
Diameter of Newton's Rings
- Bright rings: The radius (rn) of the nth bright ring is given by
r<sub>n</sub><sup>2</sup> = (2n - 1)λR/(2μ), where R is the radius of curvature of the plano-convex lens. The diameter (Dn) is thenD<sub>n</sub> = √[2(2n - 1)λR/μ]. For air (μ=1),D<sub>n</sub> = √[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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