In deriving the single slit diffraction pattern, it was stated that the intensity is zero at angles of $\text{n}\lambda/\text{a}.$ Justify this by suitably dividing the slit to bring out the cancellation.
Exercise
Download our app for free and get started
Let the slit width 'a' be divided into n equal parts of width 'a' so that,
$\text{a}'=\frac{\text{a}}{\text{n}}$
i.e., a = na'
Then,
$\text{Angle},\ \theta=\frac{\text{n}\lambda}{\text{a}}=\frac{\text{n}\lambda}{\text{na}'}$
$\text{i.e.},\ \theta=\frac{\lambda}{\text{a}'}$
At this derived angle, each slit will make first diffraction minimum. Hence, the resultant intensity for all slits will be zero at an angle of $\frac{\text{n}\lambda}{\text{a}}.$
$\text{a}'=\frac{\text{a}}{\text{n}}$
i.e., a = na'
Then,
$\text{Angle},\ \theta=\frac{\text{n}\lambda}{\text{a}}=\frac{\text{n}\lambda}{\text{na}'}$
$\text{i.e.},\ \theta=\frac{\lambda}{\text{a}'}$
At this derived angle, each slit will make first diffraction minimum. Hence, the resultant intensity for all slits will be zero at an angle of $\frac{\text{n}\lambda}{\text{a}}.$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1View SolutionDefine wavefront of a travelling wave. Using Huygens principle, obtain the law of refraction at a plane interface when light passes from a denser to rarer medium.
- 2View SolutionCalculate the radius of curvature of an equi-concave lens of refractive index 1.5, when it is kept in a medium of refractive index 1.4, to have a power of -5D?
- 3View SolutionAnswer the following question:
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? - 4Define the term 'Half-life' of a radioactive substance. Two different radioactive substances have half-lives $T_1$ and $T_2$ and number of undecayed atoms at an instant $N_1$ and $N_2$, respectively. Find the ratio of their activities at that instant.View Solution
- 5View SolutionWhether the diffraction effects from a slit will be more clearly visible or less clearly, if the slit-width is increased?
- 6View SolutionDraw the output waveform at X, using the given inputs A and B for the logic circuit shown below. Also, identify the logic operation performed by this circuit.
- 7View SolutionAnswer the following question:
As you have learnt in the text, the principle of linear superposition of wave displacement is basic to understanding intensity distributions in diffraction and interference patterns. What is the justification of this principle? - 8An equilateral glass prism has a refractive index 1.6 in air. Calculate the angle of minimum deviation of the prism, when kept in a medium of refractive index $\frac{4\sqrt2}{5}.$View Solution
- 9View SolutionIs it necessary to have two waves of equal intensity to study interference pattern? Will there be an effect on clarity if the waves have unequal intensity?
- 10The short wavelength limit for the Lyman series of the hydrogen spectrum is 913·4 $\mathring{\text{A}}$ Calculate the short wavelength limit for Balmer series of the hydrogen spectrum.View Solution