Chapter 27: Q23PE (page 997)

How many lines per centimeter are there on a diffraction grating that gives a first-order maximum for $470 ‐ nm$ blue light at an angle of $25 . 0^{\circ}$ ?

Short Answer

Expert verified

The lines per cm for the first-order maximum are $8929$ per centimeter.

Step by step solution

Given data

$λ = 470 nm (\frac{10^{‐ 9} m}{1 nm}) = 4 . 70^{,} 10^{‐ 7} m$

The wavelength of the blue light is

The order of maximum is 1.

The angle at which the first-order maximum is observed $_{25 . 0^{\circ}}$

Evaluating the lines per centimeter for first-order maximum

The equation of the constructive interference can be expressed as

$d sinθ = mλ$ …………………(1)

Where, $d, λ, θ$ and m is the separation between slits, the wavelength of the incident light, and the angle made with the maximum and order of maximum, respectively.

Therefore, if we substitute the given data in equation (1) for m=1, we will get,

We then evaluate the number of lines per centimeter, $n$ , using the relation:

$n = \frac{1.0 cm}{d}$ .

Substitute the value in the above expression, and we get,

$n = (\frac{1.0 cm}{1.12 \times 10^{‐ 6} m}) (\frac{1 m}{100 cm}) \approx 8929$

Therefore, the lines for the first-order maximum are $^{8929}$ per centimeter.

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How many lines per centimeter are there on a diffraction grating that gives a first-order maximum for $470 ‐ nm$ blue light at an angle of $25 . 0^{\circ}$ ?

Short Answer

Step by step solution

Given data

Evaluating the lines per centimeter for first-order maximum

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How many lines per centimeter are there on a diffraction grating that gives a first-order maximum for 470‐nmblue light at an angle of25.0∘?

Short Answer

Step by step solution

Given data

Evaluating the lines per centimeter for first-order maximum

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Solid State Physics

Electricity

Physics of Motion

Physical Quantities And Units

Fundamentals of Physics

Atoms and Radioactivity

Study anywhere. Anytime. Across all devices.

How many lines per centimeter are there on a diffraction grating that gives a first-order maximum for $470 ‐ nm$ blue light at an angle of $25 . 0^{\circ}$ ?