Question
Consider a set of two slits each of width $b=5 \times 10^{-2} \mathrm{~cm}$ and separated by a distance $d=0.1 \mathrm{~cm}$, illuminated by a monochromatic light of wavelength $6.328 \times 10^{-5} \mathrm{~cm} .$ If a convex lens of focal length $10 \mathrm{~cm}$ is placed beyond the double slit arrangement, calculate the positions of the minima inside the first diffraction minimum.
Step 1
Step 1: The condition for the diffraction minimum is given by $\sin \theta = \frac{m + \frac{1}{2}}{d} \lambda$, where $m$ is the order of the minimum, $d$ is the distance between the slits, and $\lambda$ is the wavelength of the light. Show more…
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Consider a set of two slits cach of width $b=5 \times 10^{-2} \mathrm{~cm}$ and separated by a distance $d=0.1 \mathrm{~cm}$, illuminated by a rnonochromatic light of wavelength $6.328 \times 10^{-5} \mathrm{~cm}$. If a coavex lens of focal length $10 \mathrm{~cm}$ is placed beyond the double slit arrangement, calculate the positions of the minima insido the first diffraction minimum.
Consider a rectangular aperture of dimensions $0.2 \mathrm{~mm} \times$ $0.3 \mathrm{~mm}$. Obtain the positions of the first few maxims and minima in the Fraunhofer diffraction pattern along directions parallel to the length and breadth of the rectengle. Assume $\lambda=5 \times 10^{-5} \mathrm{~cm}$ and that the diffraction pattern is produced at the focal plane of a lens of focal length $20 \mathrm{~cm}$.
Consider a rectangular aperture of dimensions $0.2 \mathrm{~mm}$ $\times 0.3 \mathrm{~mm}$. Obtain the positions of the first few maxima and minima in the Fraunhofer diffraction pattern along directions parallel to the length and breadth of the rectangle. Assume $\lambda=5 \times 10^{-5} \mathrm{~cm}$ and that the diffraction pattern is produced at the focal plane of a lens of focal length $20 \mathrm{~cm}$. [Ans: Along the $x$ -axis, minima will occur at $x \approx 0.05$, $0.10,0.15, \ldots \mathrm{cm} ;$ along the $y$ -axis, minima will occur at $$ y \approx 0.033,0.067,0.1, \ldots \mathrm{cm}] $$.
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