Explanation​:
The wave is faster in medium $Y$ than in medium $X$. As a result, the ray representing the wave is expected to bend away from the normal, refracting into the original medium.

If the angle of incidence exceeds the critical angle, however, the angle of refraction will be undefined and the wave will undergo total internal reflection.

This is exactly what is shown by Option D, which is the correct response.

Option A shows the ray bending towards the normal, Option C shows no bending at all, and Option B shows an impossible path for the wave to travel.

Explanation​:
Speed is always positive and it should have maximum and minimum values twice in one complete oscillation. Therefore the answer is C.

Explanation​:

The angular width of the first maximum;

• θ=λ/b​

The central maximum has the twice angular width of the first maximum;

• θc=2λ/b​

Since wavelength λ and slit width b are not changed, the angular width must be constant. Therefore, the answer is C.

Given that the angular width is constant, increasing the distance D will cause the size of the central maximum on the screen to double, which indicates that option A is incorrect.

The interference pattern is not modulated by the single slit diffraction when slit width is negligible. Therefore, the intensities for all maxima should be the same. A decrease in slit width results in a decrease of maximum intensity. Therefore the peak values should be smaller.

Explanation​:
C: Correct. In simple harmonic motion, acceleration and displacement always have opposite directions and are proportional

A: Incorrect. Since total energy is the sum of kinetic and potential energies, and the total energy is conserved, so at the time kinetic energy is zero the potential energy must have the maximum value. Since that's not represented in graphs I and II, A is not a correct answer

B: Incorrect. Velocity will be zero at positions of maximum magnitude of acceleration, considering that acceleration and displacement are proportional in magnitude and opposite in direction. So B is not a correct answer.

D: Incorrect The graph of velocity variation with time can be concluded from the slope of displacement variation with time, so the velocity will be zero at positions of maximum magnitude of displacement. Which makes D not a correct answer.

Explanation​:
Since frequency is 0.05 Hz, T=1/f=1/0.05=20 s

The amplitude is $4cm$ on either side of the equilibrium position because in one full cycle it travels four amplitudes (16/4=4 cm

Explanation​:
Acceleration is proportional to the resultant force. Therefore, force and acceleration must be in the same direction.

Explanation​:

Doppler effect only occurs when there is relative motion between the observer and the source. In this case, the satellite and receiver are motionless relative to each other. Therefore, there will be no change in frequency.

Explanation​:

The single slit diffraction effect can not be ignored when slit width is not negligible. Therefore, there will be modulation of the interference pattern. Greater slit widths allow more light reach to screen and makes the fringes brighter. The fringe width is dependent on wavelength, slit separation and distance between screen and slits. None of them have changed. Therefore the fringe width is not affected.

Explanation​:
The fringe separation equation is given by s=λD/d​ where $s$ is the fringe separation, $\lambda$ is the wavelength, $D$ is the distance between the double slit barrier and the screen and s is the distance between the two slits on the double slit barrier. The question is asking which change will increase the value of s.

• A. Moving the screen closer to the double slit barrier will decrease D. Since $D$ is directly proportional to $s$, $s$ will also decrease.
• B. Violet light has a higher frequency / shorter wavelength than blue light. Using violet light instead of blue light will decrease the value of $\lambda$, and since $\lambda$ is also directly proportional to $s$, $s$ will subsequently decrease.
• C. Since $d$, the space between the two slits on the double slit barrier, is inversely proportional to $s$, as $d$ decreases, $s$ will increase.
• D. As long as the aperture is not completely closed, it will have no bearing on the spacing of the double slit interference pattern and will only reduce its intensity. The purpose of the single slit is to produce coherent light through diffraction, which then falls on the double slits.

Explanation​:
Sound travels faster in water. According to Snell's law, the waves will refract away from the normal as seen in options $A$ and $C$.

Because $v=f\lambda$ and f is constant across the boundary, favelength also increases when the speed increases as seen in choices $B$ and C.

Therefore C is the correct answer.

Explanation​:
The y axis cannot represent the velocity of the pendulum, as a velocity-position graph would also show negative velocities to represent motion in both directions.

The formula for kinetic energy is given by 1/2mω^2(0x^2 −x2), which would be parabolic in shape, opening downwards as is shown in the graph.

The potential energy of the bob should be less at the equilibrium position than in the positions where displacement is maximum.

Explanation​:
Light will refract away from the normal at a boundary where there is an increase in speed as in a glass to air boundary. Answers A and C show this. A light ray will not refract at a boundary if its angle of incidence is 0°. It must therefore enter the curved edge aligned with the center of the straight side as in A. Therefore the answer is A.

Explanation​:
Two conditions must be satisfied to define motion as simple harmonic motion;

• The acceleration is proportional to the displacement.
• The acceleration and displacement are in opposite directions.

The second condition indicates the existence of a negative sign in front of the displacement and the first condition demands to have $x$ instead of x^2 in the expression. These two conditions are satisfied in B.

Explanation​:
Recall for simple harmonic motion, a ∝−x, therefore the object experiences maximum negative acceleration at maximum positive displacement from equilibrium.