Please help !

Finish the following statement:
"The greater the number of lines on a diffraction grating of a given size,"

a)the greater
b)smaller

then

a)the range of wavelengths that can be diffracted
b)the distance between the bright fringes produced

a,b

"The greater the number of lines on a diffraction grating of a given size, the greater the range of wavelengths that can be diffracted. And the distance between the bright fringes produced? Well, it's just a reminder to always carry your measuring tape, or you might end up in a 'fringe' situation. Remember, accuracy is key!"

The greater the number of lines on a diffraction grating of a given size, the greater the range of wavelengths that can be diffracted.

To complete the statement, we need to determine the relationship between the number of lines on a diffraction grating and the two given options. Let's break it down:

"The greater the number of lines on a diffraction grating of a given size,"

a) the greater
b) smaller

then

a) the range of wavelengths that can be diffracted
b) the distance between the bright fringes produced

To understand the relationship, we need to consider the fundamental principles of a diffraction grating. A diffraction grating is a surface with closely spaced lines that can diffract light. When light passes through a diffraction grating, it undergoes constructive and destructive interference, producing bright and dark fringes.

The key factor here is the number of lines on the grating. As the number of lines increases, the spacing between the lines decreases. This means that more lines will be packed into the same given size of the grating.

Now let's analyze each option:

a) the range of wavelengths that can be diffracted
When the number of lines on a diffraction grating increases, the range of wavelengths that can be diffracted also increases. This is because the spacing between the lines decreases, allowing the grating to diffract shorter wavelengths (higher frequencies) of light. Therefore, the correct answer is option a) the greater.

b) the distance between the bright fringes produced
As the number of lines on a diffraction grating increases, the distance between the bright fringes produced will be smaller. This is because the spacing between the lines is reduced, causing the angle between the diffracted beams to decrease, ultimately leading to a smaller distance between the bright fringes. Therefore, the correct answer is option b) smaller.

In conclusion, the correct completion of the statement is:
"The greater the number of lines on a diffraction grating of a given size, the greater the range of wavelengths that can be diffracted, and the distance between the bright fringes produced is smaller."