Problems Involving Shadows

Concept Explanation

Problems Involving Shadows

A shadow is a dark area where light from a light source is blocked by an opaque object. It occupies all of the three-dimensional volume behind an object with light in front of it. The cross section of a shadow is a two-dimensional silhouette, or a reverse projection of the object blocking the light.

Problems Involving Shadows : Shadows are formed when the person is obstructing the path of light. In the morning as the Sun rises from the East.

If a person facing towards Sun that is East, the shadow will be towards his back or in West.

If a person facing towards South, the shadow will be towards his right. that is West

If a person facing towards West, the shadow will be towards his front. or West

If a person facing towards North, the shadow will be towards his left which is West

But in the evening as we know the sets in the West. All these directions will be reversed.

When two persons facing each other during sunrise, the shadow of both are formed at the left of the person facing north.

When two persons facing each other during sunrise, the shadow of both are formed at the right of the person facing south.

When two persons facing each other during sunset, the shadow of both are formed at the right of the person facing north.

When two persons facing each other during sunset, the shadow of both are formed at the left of the person facing south.

Illustration : In an evening when Suraj started walking from his house, his shadow was exactly towards his right. He walked 6 km. Then he turns to his left and moved 4 km. Again he turns to his right and walked 6 km. Then he turns to his right and moved 13 km. How far is he and in which direction from the starting point ?

A. 15 km North-East B. 15 km North C. 15 km South-East D. 16 km South E. 17 km East

Answer : A

Solution : In the evening when the Sun is in the West the shadow is in East In an evening when Suraj started walking from his house, his shadow was exactly towards his right. that means he is facing in North Direction.

Then He reaches point B after traversing a distance of 6 Km

Then he turns to his left and moved 4 km and reaches point C.

Again he turns to his right and walked 6 km and reaches point D

Then he turns to his right and moved 13 km and reaches point E

The path he has traversed is shown in the figure below

The distance between A and E is calculated using pythagoras theorem

We see that $Delta$ AFE is a right angled triangle, right angled at F. So AE is the hypotenuse as it is the side opposite to right angle.

$AF= AB + CD = 6 + 6 = 12; km$

$FE = DE - BC = 13 - 4 = 9 km$

$EA = sqrt {AF^2+EF^2}=sqrt {12^2+9^2}$

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Sample Questions

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Question : 1

At sunrise, Rohit and Mohit are having a conversation standing in front of each other. The shadow of Mohit is formed towards the right hand of Rohit. What direction is Mohit facing?
A. East	B. West	C. North	D. South
Right Option : C
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Question : 2

One morning A and B were standing opposite to each other. The shadow of A fell exactly on his left. Towards which direction does B facing?
A. East	B. West	C. North	D. South
Right Option : D
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Question : 3

One morning P and Q were talking to each other face to face. If shadow of P was exactly to right of P, then which direction was Q facing?
A. East	B. West	C. North	D. South
Right Option : C
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