List of top Communication and Optical Instrumentation Questions asked in GATE IN

Consider 24 voice signals being transmitted without latency using time-division multiplexing. If each signal is sampled at 12 kHz and represented by an 8-bit word, the bit-duration (in microseconds) is _________ (round off to two decimal places)
A photodiode is made of a semiconductor with a bandgap of 1.42 eV. Given that Planck’s constant is \(6.626 \times 10^{-34}\) J·s, the speed of light in vacuum is \(3 \times 10^8\) m/s, and \(1 \, \text{eV} = 1.6 \times 10^{-19}\) J, the cut-off wavelength (in nanometers) of the photodiode is _________ (round off to one decimal place).

A sinusoidal carrier wave with amplitude \( A_c \) and frequency \( f_c \) is amplitude modulated with a message signal \( m(t) \) having frequency \( 0<f_m \ll f_c \) to generate the modulated wave \( s(t) \) given by \[ s(t) = A_c[1 + m(t)]\cos(2\pi f_c t) \] The message signal that can be retrieved completely using envelope detection is _________

A laser pulse is sent from ground level to the bottom of a concrete water tank at normal incidence. The tank is filled with water up to 2 m below the ground level. The reflected pulse from the bottom of the tank travels back and hits the detector. The round-trip time elapsed between sending the laser pulse, the pulse hitting the bottom of the tank, reflecting back and sensed by the detector is 100 ns. The depth of the tank from ground level marked as \( x \) in metre is \(\underline{\hspace{2cm}}\) . 

In the figure shown, a large multimode fiber with \( n_{\text{core}} = 1.5 \) and \( n_{\text{clad}} = 1.2 \) is used for sensing. A portion with the cladding removed passes through a liquid with refractive index \( n_{\text{liquid}} \). An LED is used to illuminate the fiber from one end and a paper is placed on the other end, 1 cm from the end of the fiber. The paper shows a spot with radius 1 cm. The refractive index \( n_{\text{liquid}} \) of the liquid (rounded off to two decimal places) is \(\underline{\hspace{2cm}}\). 

A signal having a bandwidth of 5 MHz is transmitted using the Pulse Code Modulation (PCM) scheme as follows. The signal is sampled at a rate of 50% above the Nyquist rate and quantized into 256 levels. The binary pulse rate of the PCM signal in Mbits per second is \(\underline{\hspace{1cm}}\).
An amplitude modulation (AM) scheme uses tone modulation, with modulation index of 0.6. The power efficiency of the AM scheme is \(\underline{\hspace{2cm}}\) % (rounded off to one decimal place).
When the movable arm of a Michelson interferometer in vacuum \( (n = 1) \) is moved by 325 \(\mu m\), the number of fringe crossings is 1000. The wavelength of the laser used in nanometers is \(\underline{\hspace{2cm}}\).