Question

How many complete orders of the visible spectrum (400nm<λ<700nm) can be produced with a diffraction grating that contains 5000 lines per centimeter?

Answer 1

A diffraction grating with 5000 lines per centimeter can produce approximately 0.92 complete orders of the visible spectrum

Step-by-step explanation:

The number of complete orders of the visible spectrum that can be produced with a diffraction grating depends on the number of lines per centimeter and the range of wavelengths. In this case, the diffraction grating contains 5000 lines per centimeter and the visible spectrum range is from 400nm to 700nm. To calculate the number of complete orders, we need to find the number of wavelengths that fit within the range of each order.

1. The first-order spectrum will contain one complete order of the visible spectrum.
2. The second-order spectrum will contain two complete orders of the visible spectrum.
3. The third-order spectrum will contain three complete orders of the visible spectrum.
4. And so on.

Since the diffraction grating has 5000 lines per centimeter, for each order, the number of wavelengths that fit within the range can be calculated using the formula: Number of orders = Number of lines per centimeter * Range of wavelengths / 10000.

Using this formula, for the range of 400nm to 700nm, the number of complete orders that can be produced with a diffraction grating that contains 5000 lines per centimeter is approximately 0.92.