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## 14.13 Resolving Power of a Plane Transmission Grating

14.13 Resolving power of a plane transmission grating The capacity of an optical instrument to show separate images of very closely placed two objects is called resolving power. The resolving … - Selection from Engineering Physics [Book]

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### 14.13 Resolving power of a plane transmission grating

The capacity of an optical instrument to show separate images of very closely placed two objects is called resolving power. The resolving power of a diffraction grating is defined as its ability to form separate diffraction maxima of two closely separated wave lengths.

The expression for resolving power of a grating can be obtained with the aid of Fig. 14.20.

Figure 14.20 Calculation of resolving power of a plane transmission granting

In Fig. 14.20, xy represents a plane transmission grating having (e + b) as grating element and N lines per unit width of grating. A light beam having two ...

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This set of Engineering Physics Multiple Choice Questions & Answers (MCQs) focuses on “Resolving Power of Grating”. 1. Which of the following is the correct expression for the resolving power of a grating? a) (nN + 1)/λ b) nN/λ c) nN/λ + 1 d) nN 2. What is the SI unit of the Resolving power ... Read more

## Engineering Physics Questions and Answers – Resolving Power of Grating

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This set of Engineering Physics Multiple Choice Questions & Answers (MCQs) focuses on “Resolving Power of Grating”.

1. Which of the following is the correct expression for the resolving power of a grating?

2. What is the SI unit of the Resolving power of a plane transmission grating?

3. The resolving power of a grating is inversely proportional to the wavelength of the incident light.

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4. Our eyes see two objects as separate, only if the angle subtended by them at the eye is greater than _________

5. The resolving power of a grating is directly proportional to grating constant.

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6. If a light is incident on a grating with 5000 lines/cm, then the angular separation of the two lines (5000 Å and 5006 Å) in first order spectrum is ______

7. Light is incident normally on a grating of width 5 X 10-3 m with 2500 lines. What is the resolving power of the grating in the second order spectrum?

8. What is the minimum number of lines per cm in a 2.5 cm wide grating spectrum which will just resolve two sodium lines (5890 Å and 5896 Å) in the first order spectrum?

9. The following pattern was observed by a plane diffraction grating. How are the two images resolved?

a) Not resolved b) Just Resolved

c) Partially resolved

10. A grating has 16000 per inch over a length of 5 inches. What will be the smallest wavelength difference for a light of wavelength 6000 Å?

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## [Solved] The resolving power of a plane transmission diffraction grat

Concept: PLANE DIFFRACTION GRATING: A diffraction grating is an extremely useful device, and one of it consists of a large number of narrow slits sid

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## The resolving power of a plane transmission diffraction grating will increase on increasing:

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the grating element only

the order of the spectrum only

the total number of rulings on the grating only

both order of the spectrum and total number of rulings on the grating

Option 4 : both order of the spectrum and total number of rulings on the grating

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## Detailed Solution

Concept:

PLANE DIFFRACTION GRATING:

A diffraction grating is an extremely useful device, and one of it consists of a large number of narrow slits side by side.

The slits are separated by opaque spaces.

When a wavefront is an incident on a grating surface, light is transmitted through the slits and obstructed by the opaque portions. Such a grating is called a transmission grating.

Resolving Power:

The capacity of an optical instrument to show separate images of very closely placed two objects is called resolving power.

The resolving power of a diffraction grating is defined as its ability to form separate diffraction maxima of two closely separated wavelengths.

If λ and λ + dλ are wavelengths of two neighboring spectral lines, the resolving power of the grating is the ratio λ/dλ.

The resolving power of the grating is given by

λdλ=nN

Where n - order of spectrum, N - total no. of lines in the given grating.

Explanation:

From the above equation, it is clear that the resolving power of the grating is directly proportional to the order of the spectrum and the total number of rulings on the grating.

∴ The resolving power of a plane transmission diffraction grating will increase on increasing both order of the spectrum and the total number of rulings on the grating.

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Last updated on Dec 22, 2022

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## More Diffraction Questions

Q1. Angular width of the central maxima in the Fraunhofer diffraction for λ = 6000 Å is θ0. When the same slit is illuminated by another monochromatic light, the angular width decreases by 30%. The wavelength of this light is,Q2. A light wave is traveling linearly in a medium of dielectric constant 4, incidents on the horizontal interface are separating the medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be : (Given : relative permeability of medium μr = 1)Q3. In a Young's double slit experiment, a student observes 8 fringes in a certain segment of screen when a monochromatic light of 600 nm wavelength is used. If the wavelength of light is changed to 400 nm, then the number of fringes he would observe in the same region of the screen is:Q4. The wavelength of an X-ray beam is 10 Å. The mass of a fictitious particle having the same energy as that of the X-ray photons is

x3

h kg. The value of x is ______.  (h = Planck's constant)

Q5. In Young’s double slit experiment, if the separation between coherent sources is halved and the distance of the screen from the coherent sources is doubled, then the fringe width becomes :Q6. Pick the wrong answer in the context with rainbow.Q7. In a double slit experiment, when light of wavelength 400 nm was used, the angular width of the first minima formed on a screen placed 1 m away, was found to be 0.2°. What will be the angular width of the first minima, if the entire experimental apparatus is immersed in water? (μwater = 4/3)Q8. In Young's double slit experiment the separation d between the slits is 2 mm, the wavelength λ of the light used is 5896 Å and distance D between the screen and slits is 100 cm. It is found that the angular width of the fringes is 0.20°. To increase the fringe angular width to 0.21° (with same λ and D) the separation between the slits needs to be changed to

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