Two transparent slabs having equal thickness but different

Question: Two transparent slabs having equal thickness but different refractive indices $\mu_{1}$ and $\mu_{2}$ are pasted side by side to form a composite slab. This slab is placed just after the double slit in a Young's experiment so that the light from one slit goes through one material and other slit goes through the other material. What should be the minimum thickness of the slab so that there is a minimum at the point $p_{0}$ which is equidistant from the slits? Solution:...

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A mica strip and a polysterene strip are fitted on the two slits

Question: A mica strip and a polysterene strip are fitted on the two slits of a double slit apparatus. The thickness of the strips is $0.50$ $\mathrm{mm}$ and the separation between the slits is $0.12 \mathrm{~cm}$. The refractive index of mica and polysterene are $1.58$ and $1.55$ respectively for the light of wavelength $590 \mathrm{~nm}$ which is used in the experiment. The interference is observed on a screen a distance one metre away. (a) What would be the fringe-width? (b) At what distance...

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Question: Differentiate each of the following w.r.t. $x$ : (i) $\tan (\log x)$ (ii) $\log (\sec x)$ (iii) $\log (\sin (x / 2))$ Solution:...

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In a Young's double slit experiment using monochromatic light,

Question: In a Young's double slit experiment using monochromatic light, the fringe pattern shifts by a certain distance on the screen when a mica sheet of refractive index $1.6$ and thickness $1.964$ micron ( 1 micron $=10^{-5} \mathrm{~m}$ is introduced in the path of one of the interfering waves. The mica sheet is then removed and the distance between the screen and slits is doubled. It is found that the distance between the successive maxima now is the same as the observed fringe-shift upon ...

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A transparent paper (refractive index=1.45) of thickness

Question: A transparent paper (refractive index=1.45) of thickness $0.02 \mathrm{~mm}$ is pasted on one of the slits of a Young's slit experiment which uses monochromatic light of wavelength $620 \mathrm{~nm}$. How many fringes will cross through the centre if the paper is removed? Solution:...

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A plate of thickness t made of a material of refractive

Question: A plate of thickness $t$ made of a material of refractive index $\mu$ is placed in front of one of the slits in a double slit experiment. (a) Find the change in the optical path due to introduction of the plate. (b) What should be the minimum thickness $t$ which will make the intensity at the centre of the fringe pattern zero? Wavelength of the light used is $\lambda$. Neglect any absorption of light in the plate. Solution:...

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Find the thickness of a plate which will produce a change

Question: Find the thickness of a plate which will produce a change in optical path equal to half the wavelength $\lambda$ of the light passing through it normally. The refractive index of the plate is $\mu$. Solution:...

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