Option 2 : 1.2/50 μs

The wave-shape of a standard lighting impulse voltage is given by 1.2/50 μs.

Option 2 : 16 cm

**Concept:**

The cut-off frequency for a rectangular waveguide with dimension ‘a (length)’ and ‘b (width)’ is given as:

\({{f}_{c\left( mn \right)}}=\frac{c}{2}\sqrt{{{\left( \frac{m}{a} \right)}^{2}}+{{\left( \frac{n}{b} \right)}^{2}}}\)

'm' and 'n' represents the possible modes.

The cut-off/critical wavelength is given as:

\({{\rm{λ }}_{\rm{C}}} = \frac{2}{{\sqrt {{{\left( {\frac{{\rm{m}}}{{\rm{a}}}} \right)}^2} + {{\left( {\frac{{\rm{n}}}{{\rm{b}}}} \right)}^2}} }}\)

**Calculation:**

Given: a = 8 cm, b = 4 cm

For H_{10} mode

i.e. m = 1 and n = 0, we get

\({{\rm{λ }}_{\rm{C}}} = \frac{2}{{\sqrt {{{\left( {\frac{{\rm{1}}}{{\rm{8}}}} \right)}^2} + {{\left( {\frac{{\rm{0}}}{{\rm{4}}}} \right)}^2}} }}\)

λ_{C} = 2 × 8 cm = 16 cm

Option 3 : -1

**Concept:**

**Traveling Waves:**

- A traveling wave is a temporary wave that creates a disturbance and moves along the transmission line at a constant speed.
- A traveling wave occurs for a short duration (for a few microseconds) but causes a much disturbance in the line. The transient wave is set up in the transmission line mainly due to switching, faults and lightning.
- The traveling wave plays a major role in knowing the voltages and currents at all the points in the power system.
- The traveling waves also help in designing the insulators, protective equipment, the insulation of the terminal equipment, and overall insulation coordination.

**Receiving the end of a transmission line terminated by a resistance**

The reflection coefficient of current given by:

\({ρ _{{i_i}}} = \frac{{{i_r}}}{{{i_i}}} = \left( {\frac{{{Z_c} - R}}{{{Z_c} - R}}} \right)\) ......(1)

Where

i_{r }= Reflected current

i_{i} = Incident current

Z_{c} = Characteristic impedance

R = Resistance

If receiving end of transmission line operated under no-load condition

R = Zero

**As the direction of reflected and incident current is opposite**

**ir = -ii**

By eq (1)

\({ρ _{{i_i}}} = \frac{{ - {i_r}}}{{{i_i}}} = \left( {\frac{{{Z_c} - 0}}{{{Z_c} - 0}}} \right)\)

ρ_{i }= -1

Option 2 : 1.2/50 μs

The wave-shape of a standard lighting impulse voltage is given by 1.2/50 μs.

Option 2 : 16 cm

**Concept:**

The cut-off frequency for a rectangular waveguide with dimension ‘a (length)’ and ‘b (width)’ is given as:

\({{f}_{c\left( mn \right)}}=\frac{c}{2}\sqrt{{{\left( \frac{m}{a} \right)}^{2}}+{{\left( \frac{n}{b} \right)}^{2}}}\)

'm' and 'n' represents the possible modes.

The cut-off/critical wavelength is given as:

\({{\rm{λ }}_{\rm{C}}} = \frac{2}{{\sqrt {{{\left( {\frac{{\rm{m}}}{{\rm{a}}}} \right)}^2} + {{\left( {\frac{{\rm{n}}}{{\rm{b}}}} \right)}^2}} }}\)

**Calculation:**

Given: a = 8 cm, b = 4 cm

For H_{10} mode

i.e. m = 1 and n = 0, we get

\({{\rm{λ }}_{\rm{C}}} = \frac{2}{{\sqrt {{{\left( {\frac{{\rm{1}}}{{\rm{8}}}} \right)}^2} + {{\left( {\frac{{\rm{0}}}{{\rm{4}}}} \right)}^2}} }}\)

λ_{C} = 2 × 8 cm = 16 cm

Option 4 : \(co{s^{ - 1}}\,\sqrt {\frac{1}{3}} \)

**Concept:**

**Wavefront:**

- The
**locus of all particles**in a medium,**vibrating**in the**same phase**is called waveFront. - The
**direction**of propagation of light (ray of light) is**perpendicular to the waveFront**.

**Equation of plane** passing through origin is given by,

ax + by + cz = r

Where a, b, c represents the direction ratio.

**Cosines ****of the angles** between the vector and the three +ve coordinate axes (**Direction cosines**) are,

\(cosα = \frac{a}{\sqrt {a^2 +b^2 + c^2}}\)

\(cos\beta = \frac{b}{\sqrt {a^2 +b^2 + c^2}}\)

\(cos\gamma = \frac{c}{\sqrt {a^2 +b^2 + c^2}}\)

__Calculation:__

Equation of wavefront represented by

x + y + z = c

This is the equation of plane, whose direction ration are

a = 1, b = 1, c = 1 so,

\(\sqrt {a^2 + b^2 + c^2} = \sqrt 3\)

Let plane make anggle α with x-axis,

\(\Rightarrow cosα = \frac{a}{\sqrt {a^2 +b^2 + c^2}}\)

\(\Rightarrow cos\alpha = \frac{1}{\sqrt3}\)

\(\Rightarrow \alpha = cos^{-1}\frac{1}{\sqrt3}\)

Hence, the **angle** made by the direction of propagation of light **with x-axis** is \( cos^{-1}\frac{1}{\sqrt3}\).