Question

Answer the following questions:
i) In a single slit diffraction experiment, the width of the slit is made double the original width. How does this affect the size and intensity of the central diffraction band?
ii) In what way is diffraction from each slit related to the interference pattern in a double-slit experiment?
iii) When a tiny circular obstacle is placed in the path of light from a distant source, a bright spot is seen at the centre of the shadow of the obstacle. Explain why?
iv) Two students are separated by a $7mm$ partition wall in a room $10m$ high. If both light and sound waves can bend around obstacles, how is it that the students are unable to see each other even though they can converse easily.
v) Ray optics is based on the assumption that light travels in a straight line. Diffraction effects (observed when light propagates through small apertures/ slits or around small obstacles) disprove this assumption. Yet the ray optics assumption is so commonly used in understanding location and several other properties of images in optical instruments. What is the justification?

Answer 1

Diffraction is the phenomenon of bending of light. When the light rays strike through any object or obstacle, they strike and bend around the corners of the obstacle. After bending, the light illuminates the areas around the object.

Complete step by step solution:
(i) In a single slit experiment, the width of central slit is denoted by ${B_o}$
${B_o} = \dfrac{{2D\lambda }}{d}$
Where D is the distance of slit from screen
$d$ is width of slit
$\lambda$ is wavelength
If the width is made double than the original width then ${d'} = 2d$
Therefore, ${B_o} = \dfrac{{D\lambda }}{d}$
The size of the diffraction band will be halved and the intensity will increase up to four times.

ii) Since it is known that the waves passing through each slit are diffracted and spread, so the double slit makes them interfere with each other and a pattern is formed. Therefore the interference pattern in each slit is modulated by diffraction.

iii) It is clear that diffraction and interference occur simultaneously. The light waves get diffracted from the edge of the obstacle and interfere to form a spot at the centre of shadow. So when a tiny circular obstacle is placed in the path of light from a distant source, a bright spot is seen at the centre of the shadow of the obstacle.

iv) The light waves are able to bend if the size of the object is similar to that of the wavelength of the waves. Students are unable to see each other because the angle of diffraction is small. This is because the size of the light waves is small as compared to the size of the wall.
The size of sound waves is similar to that of the size of the wall. So the sound waves bend at a larger angle. So the students are able to hear each other.

v) Ray optics is used in understanding locations and several other optical instruments because the size of the aperture is comparatively larger than the wavelength of light used.

Note: It is to be noted that optics is the branch of physics that studies the interaction of light waves and its properties. The phenomenon such as reflection, refraction, diffraction and interference are all the parts of optics. It is the study of how light is generated, propagated and detected.