Monochromatic light is normally incident on a diffraction grating. The mth order line is at a angle of diffraction θ and has width w. A wide single slit is now placed in front of the grating and its width is then slowly reduced. As a
the ans. is: θ remains the same and w increases
Can someone help me solve this?
To solve this problem, let's break it down step by step:
1. First, we need to understand the concept of a diffraction grating. A diffraction grating is an optical device consisting of a surface with a large number of equally spaced parallel slits or rulings. When monochromatic light (light of a single wavelength) is incident on a diffraction grating, it diffracts and produces a pattern of bright spots called diffraction orders.
2. The angle of diffraction, denoted as θ, is the angle between the incident light ray and the diffracted ray. In this problem, the mth order line refers to the specific diffraction order that we are interested in. The angle θ is measured with respect to the normal (perpendicular) to the grating surface.
3. Now, let's consider the effect of placing a wide single slit in front of the diffraction grating and slowly reducing its width. When the slit is wide, it allows a large range of incident angles to reach the grating, resulting in a wider diffraction pattern.
4. As we reduce the width of the slit, the range of incident angles becomes smaller. However, the angle of diffraction for a specific order (in this case, the mth order line) remains the same. This is because the angle of diffraction depends primarily on the spacing between the rulings on the grating and the wavelength of light, not the width of the slit.
5. Thus, as we decrease the width of the slit, the diffraction pattern becomes narrower, resulting in a decrease in the width (w) of the mth order line. However, the angle θ remains the same.
Therefore, the answer is that θ remains the same, while the width (w) of the mth order line increases as the width of the single slit is slowly reduced.