Two thin wires, Wire-1 of diameter 0.650 mm and Wire-2 of unknown diameter d are given. To obtain the value of d, the diameters of the two wires are measured with a screw gauge. The screw gauge has a pitch of 0.5 mm and there are 100 divisions on the circular scale (CS). The smallest division on the linear scale (LS) is 0.5 mm. The table shows the readings of LS and CS for the measurements. The value of d (in µm) is :

In a single slit diffraction experiment, a slit of width $(0.016 \pm 0.002)$ mm is used to measure the wavelength of a monochromatic light source. In the diffraction pattern, the angular distance between the central maximum and first minimum is measured to be $(2^{\circ} \pm 40')$. The value of the fractional error in the measurement of wavelength is :

[Given : $\sin(2^{\circ}) = 0.035$]

As shown in the figure, a ray AB of unpolarized light enters from water of refractive index $n_w = \frac{4}{3}$ into a medium of refractive index $n_p = \frac{4}{\sqrt{3}}$ after passing through a glass plate of refractive index $n_g = 1.5$ and a layer of water. At a particular incident angle $i$ the reflected ray CD is polarized in the direction as shown in the figure. The value of $i$ (in degrees) is :

As shown in the figure, the resistance of a galvanometer G can be found by the half-deflection method. Here the resistance R₂ is adjusted such that when the key K is closed the deflection in the galvanometer becomes half of the value as compared to when K is open. Half-deflection is obtained at R₂ = 4 $\Omega$ and thus the galvanometer resistance is found to be 6 $\Omega$. In this half-deflection condition the current (in mA) through the resistor R₁ is :