The intensity pattern formed by a diffraction grating of N slits is where θ is the...

The intensity pattern formed by a diffraction grating of N slits is

where θ is the angle of diffraction. The radiation reaches the grating at normal incidence.

Using the formula above and m = 0, ±1, ±2 ... and p = an integer ≠ mN

show that
- the interference maxima occur for β = mπ
- and minima occur for β = pπ/N .
show that the orders m=pd/a (of interference) are missing if d/a is an integer .

Solutions

Expert Solution

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

A double-slit diffraction pattern is formed on a distant screen. If the separation between the slits...

A double-slit diffraction pattern is formed on a distant screen. If the separation between the slits decreases, what happens to the distance between interference fringes? Assume the angles involved remain small. The distance between interference fringes remains the same. The effect cannot be determined unless the distance between the slits and the screen is known. The distance between interference fringes also decreases. The distance between interference fringes increases.

A diffraction grating is made up of slits of width a with separation d. The grating...

A diffraction grating is made up of slits of width a with separation d. The grating is illuminated by monochromatic plane waves of wavelength λ at normal incidence. What is the angular width of a spectral line observed in the first order if the grating has N slits? State your answer in terms of the given variables. Δθw =

The diffraction pattern of two slits is imaged on a screen far from the slits. Which...

The diffraction pattern of two slits is imaged on a screen far from the slits. Which one of the following statements is true? (a) The absolute maximum intensity is located an equal distance from both slits. (b) There is only one local maximum. (c) Destructive interference occurs at a point an equal distance from two slits. (d) There is only one point where destructive interference occurs.

Light shines on a diffraction grating with a 4000 rulings (slits) per cm, which is immersed...

Light shines on a diffraction grating with a 4000 rulings (slits) per cm, which is immersed in water (refractive index=1.33), resulting in a 3rd order spectral line at a diffraction angle of 35 degrees. What is the wavelength of the light in air?

a diffraction grating has 400 slits in total. would you be able to resolve the sodium...

a diffraction grating has 400 slits in total. would you be able to resolve the sodium doublet in the 3rd order with this grating? explain the wavelengths of the sodium doublet are 589nm and 589.6nm Question 2 In a diffraction pattern due to double slits, the third order interference maxima falls on the first order diffraction minima. What is the relationship between slot srparation and slit width. Two slits are identical

a diffraction grating has 650 slits/mm. what is the highest order that contains the entire visible...

a diffraction grating has 650 slits/mm. what is the highest order that contains the entire visible spectrum?

Visible light passes through a diffraction grating that has 900 slits per centimeter, and the interference...

Visible light passes through a diffraction grating that has 900 slits per centimeter, and the interference pattern is observed on a screen that is 2.80m from the grating. In the first-order spectrum, maxima for two different wavelengths are separated on the screen by 3.10mm . What is the difference between these wavelengths? in meters

A diffraction grating with (354+ A) lines per mm is used to form an interference pattern...

A diffraction grating with (354+ A) lines per mm is used to form an interference pattern on a screen placed (45.0 + B) cm from the grating. The second-order maximum is observed at (24.6 + C) cm from the central maximum. Find the wavelength of the light. Give your answer in nanometers (nm) with 3 significant figures. A= 41 B= 6 C= 1 Vertically polarized light with an intensity of (763 + A) W/m2 passes through two polarizing filters. The...

Suppose a certain wavelength of light falls on a diffraction grating and creates an interference pattern....

Suppose a certain wavelength of light falls on a diffraction grating and creates an interference pattern. What happens to the interference pattern if the same light falls on a grating that has more lines per centimeter? What happens to the interference pattern if a longer-wavelength light falls on the same grating? Suppose a feather appears green but has no green pigment. Explain in terms of diffraction. Why is the index of refraction always greater than or equal to 1? Draw...

A 1.2-cm-wide diffraction grating has 1000 slits. It is illuminated by light of wavelength 510 nm....

A 1.2-cm-wide diffraction grating has 1000 slits. It is illuminated by light of wavelength 510 nm. What are the angles of the first two diffraction orders? Answer = ∘,∘

Subjects