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Light: Shadows and Reflections - Periscope

Grade 7CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A periscope is an optical instrument that allows an observer to see objects that are not in their direct line of sight, such as looking over a wall or from a submarine.

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The periscope works on the principle of the Reflection of Light.

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It typically consists of a tube with two plane mirrors fixed at each end. These mirrors are placed parallel to each other and inclined at an angle of 45∘45^\circ to the frame of the tube.

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According to the Laws of Reflection, the angle of incidence (∠i)(\angle i) is always equal to the angle of reflection (∠r)(\angle r).

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Light from an object enters the top of the periscope, strikes the first mirror at 45∘45^\circ, and reflects at 45∘45^\circ, causing the light to travel vertically downwards (a 90∘90^\circ turn).

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The light then strikes the second mirror at the bottom at 45∘45^\circ and reflects again at 45∘45^\circ, turning another 90∘90^\circ to enter the observer's eye.

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The final image seen through a periscope is virtual and erect.

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Periscopes are used in submarines to see above the water's surface, in tanks to view the surroundings from inside, and by soldiers in trenches.

📐Formulae

∠i=∠r\angle i = \angle r

Angle of Mirror Placement=45∘\text{Angle of Mirror Placement} = 45^\circ

Total Deviation=90∘+90∘=180∘\text{Total Deviation} = 90^\circ + 90^\circ = 180^\circ

💡Examples

Problem 1:

In a DIY periscope, if the light ray from an object strikes the first mirror at an angle of incidence of 45∘45^\circ, calculate the angle of reflection. Also, determine the total degree of turn the light ray undergoes after hitting both mirrors.

Solution:

The angle of reflection is 45∘45^\circ, and the total turn is 180∘180^\circ relative to the vertical path within the tube.

Explanation:

According to the Law of Reflection, the angle of incidence is equal to the angle of reflection: ∠i=∠r\angle i = \angle r. If ∠i=45∘\angle i = 45^\circ, then ∠r=45∘\angle r = 45^\circ. Each mirror causes the light to turn by an angle of 90∘90^\circ (calculated as ∠i+∠r\angle i + \angle r). Since there are two mirrors, the total turn is: 90+90180\begin{array}{r} 90 \\ + 90 \\ \hline 180 \end{array} degrees.

Problem 2:

Why are the mirrors in a periscope placed at an angle of 45∘45^\circ?

Solution:

The mirrors are placed at 45∘45^\circ to ensure the light ray reflects at a 90∘90^\circ angle.

Explanation:

When light hits a mirror at 45∘45^\circ relative to the surface normal, the angle of reflection is also 45∘45^\circ. The total angle between the incident ray and the reflected ray is 45∘+45∘=90∘45^\circ + 45^\circ = 90^\circ. This allows the light to travel straight down the tube and then straight out to the eye.