Wave Optics Set-3

Q1. In Young's double-slit experiment the slit separation is $d=0.50\ \mathrm{mm}$ and the screen is at distance $D=1.20\ \mathrm{m}$. Monochromatic light of wavelength $\lambda=600\ \mathrm{nm}$ is used. A thin transparent sheet of refractive index $n=1.50$ and thickness $t=1.20\ \mu\mathrm{m}$ is introduced in front of one slit. By how many fringe widths does the central bright fringe shift on the screen?

Q2. A single slit is illuminated by monochromatic light of wavelength $\lambda=500\ \mathrm{nm}$. On a screen at distance $D=1.0\ \mathrm{m}$ the width of the central diffraction maximum (distance between the first minima) is measured to be $3.0\ \mathrm{mm}$. Using small-angle approximations, the slit width $a$ is approximately:

Q3. An oil film of refractive index $n=1.25$ coats a glass substrate ($n_s=1.50$). Light is incident normally from air. Considering phase changes on reflection, the condition for constructive interference in the light reflected from the film is:

Q4. In the combined interference–diffraction pattern of two identical slits (each of width $a$ and centre separation $d$) it is observed that every third interference maximum (i.e., $m=\pm3,\pm6,\dots$) is missing from the observed fringes. Assuming normal incidence, the ratio $d/a$ is:

Q5. Assertion (A): If two narrow slits are illuminated by an extended source of finite width, the interference fringes disappear when the source width exceeds a certain limit.
Reason (R): This happens because temporal coherence of the source decreases as the source width increases.

Q6. Two closely spaced sodium lines at wavelengths $589.0\ \mathrm{nm}$ and $589.6\ \mathrm{nm}$ are to be resolved using the second order ($m=2$) of a diffraction grating. Using the Rayleigh resolving power $R=mN$ (where $N$ is the number of illuminated slits), the minimum number of slits required is approximately:

Q7. The normalized intensity distribution of single-slit diffraction shows the first minima at an angular position $\theta_1=0.010\ \mathrm{rad}$. If the incident light has wavelength $\lambda=600\ \mathrm{nm}$, the slit width $a$ is approximately (use $a\sin\theta_1=\lambda$ and small-angle approximation):

Q8. Unpolarized light of intensity $I_0$ is incident on three ideal polarizers placed in series. The transmission axis of the first polarizer is vertical, the second's axis is at $30^\circ$ to the first, and the third's axis is at $60^\circ$ to the first. The intensity transmitted through all three polarizers is:

Q9. Assertion (A): In Newton's rings observed in reflected light using a plano-convex lens on a plane glass plate the central spot is dark.
Reason (R): At the point of contact (centre) the optical path difference between the two reflected rays is zero.

Q10. Two point sources separated by angular separation $0.50\ \mathrm{arcsec}$ are to be just resolved at wavelength $\lambda=500\ \mathrm{nm}$ by a telescope with a circular aperture. Using the Rayleigh criterion $\theta=1.22\lambda/D$, the minimum aperture diameter $D$ required is approximately: