Wave Optics Set-2

Q1. In a Young's double‑slit experiment the slits are separated by $d=0.8\ \text{mm}$ and the screen is at $D=1.5\ \text{m}$. Monochromatic light of wavelength $\lambda=600\ \text{nm}$ is used. A thin transparent plate of refractive index $\mu=1.5$ is placed in front of one slit and the central maximum shifts by three bright fringes towards that slit. The thickness $t$ of the plate is closest to:

Q2. A single slit of width $a$ is illuminated by light of wavelength $\lambda$ and the Fraunhofer pattern is observed at distance $D$. The central maximum has width $W$ (distance between first minima) and peak intensity $I_{\max}$. If the slit width is reduced to $a/2$ and the wavelength is changed to $2\lambda$, keeping the incident intensity per unit area unchanged, the new central width and new peak intensity (relative to original) are respectively:

Q3. In a double‑slit experiment with slit width $a$ and slit separation $d$ ($d>a$), the observed interference pattern is modulated by a single‑slit envelope such that every 5th bright fringe is essentially missing (i.e., coincides with an envelope minimum). The ratio $d/a$ is therefore approximately:

Q4. 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 between lens and plate the geometrical path difference between the two reflected rays is zero.

Q5. In Newton's rings (reflected light, central dark) produced by a plano‑convex lens on a glass plate with $\lambda=600\ \text{nm}$, the diameter of the 10th dark ring is $4.00\ \text{mm}$. The radius of curvature $R$ of the lens is approximately:

Q6. A plane diffraction grating has $5000$ lines per centimetre. Monochromatic light of wavelength $\lambda=480\ \text{nm}$ is incident normally. The maximum observable diffraction order $n_{\max}$ is:

Q7. Unpolarized light of intensity $I_0$ is incident on an ideal linear polarizer whose axis is horizontal. The transmitted beam then passes through an ideal quarter‑wave plate whose fast axis is also horizontal, and finally through an analyzer with transmission axis vertical (i.e. perpendicular to the initial polarizer). The intensity transmitted after the analyzer is:

Q8. A single slit is illuminated with light of wavelength $\lambda=500\ \text{nm}$ and the diffraction pattern is observed on a screen at $D=1.20\ \text{m}$. The distance between the first minima on either side of the central maximum (central maximum width) is measured to be $6.0\ \text{mm}$. The slit width $a$ is approximately:

Q9. Assertion (A): For a diffraction grating, increasing the number of illuminated lines (keeping the grating spacing $d$ constant) makes the principal maxima sharper and increases the resolving power.
Reason (R): For a single slit the minima occur at $a\sin\theta=m\lambda$.

Q10. In a Michelson interferometer the source is nearly monochromatic with mean wavelength $\lambda=600\ \text{nm}$ consisting of two very close spectral lines. The fringe visibility is observed to be maximum periodically as the movable mirror is displaced; successive visibility maxima occur when the mirror is displaced by $\Delta d=6.0\ \text{mm}$. The approximate separation $\Delta\lambda$ between the two spectral lines is: