Answer
Verified
109.8k+ views
Hint:When a plane mirror reflects a ray of light, the angle of reflection is always equal to the angle of incidence. The ray of incidence, reflection and the normal all lie on the same plane. This principle will help us solve the problem in hand. If an incident ray subtends a certain angle then this means that that angle represents the sum of both reflected angle and incident angle.
Complete step by step solution:
Let’s first analyse the scenario. The mirror is at a distance of $60m$ from the foot of the tower.
The incident ray from the top of the tower will hit the mirror to subtend an angle of $90^\circ $. This means that when the incident ray, coming from the tip of the tower hits the mirror it creates a $45^\circ $ angle with the normal and the angle of reflection is $45^\circ $. This is because reflection is based on the principle that angle of reflection is equal to the angle of incidence.
Let’s look at the following figure for better understanding.
From the figure we can see that in the right angled triangle $\vartriangle ABC$ the value of angle $\angle C$ is $45^\circ $.
This implies that the right-angled triangle is an isosceles triangle too. So the lengths of arms $\overline {AB} $ and $\overline {BC} $ are equal.
So the height of the tower will be $\left| {\overline {AB} } \right| = \left| {\overline {BC} } \right| = 60m$
Thus our correct answer is option (B).
Note:Any kind of reflecting surface works on the principle that angle of incidence is equal to angle of reflection. In some cases we might need to use trigonometric calculations in order to find an angle or length of an arm.
Complete step by step solution:
Let’s first analyse the scenario. The mirror is at a distance of $60m$ from the foot of the tower.
The incident ray from the top of the tower will hit the mirror to subtend an angle of $90^\circ $. This means that when the incident ray, coming from the tip of the tower hits the mirror it creates a $45^\circ $ angle with the normal and the angle of reflection is $45^\circ $. This is because reflection is based on the principle that angle of reflection is equal to the angle of incidence.
Let’s look at the following figure for better understanding.
From the figure we can see that in the right angled triangle $\vartriangle ABC$ the value of angle $\angle C$ is $45^\circ $.
This implies that the right-angled triangle is an isosceles triangle too. So the lengths of arms $\overline {AB} $ and $\overline {BC} $ are equal.
So the height of the tower will be $\left| {\overline {AB} } \right| = \left| {\overline {BC} } \right| = 60m$
Thus our correct answer is option (B).
Note:Any kind of reflecting surface works on the principle that angle of incidence is equal to angle of reflection. In some cases we might need to use trigonometric calculations in order to find an angle or length of an arm.
Recently Updated Pages
If x2 hx 21 0x2 3hx + 35 0h 0 has a common root then class 10 maths JEE_Main
The radius of a sector is 12 cm and the angle is 120circ class 10 maths JEE_Main
For what value of x function fleft x right x4 4x3 + class 10 maths JEE_Main
What is the area under the curve yx+x1 betweenx0 and class 10 maths JEE_Main
The volume of a sphere is dfrac43pi r3 cubic units class 10 maths JEE_Main
Which of the following is a good conductor of electricity class 10 chemistry JEE_Main
Other Pages
Electric field due to uniformly charged sphere class 12 physics JEE_Main
The adjoining diagram shows the spectral energy density class 11 physics JEE_MAIN
In a steady state of heat conduction the temperature class 11 physics JEE_Main
If a wire of resistance R is stretched to double of class 12 physics JEE_Main