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Chapter 16: Problem 2240

If a ray of light is incident on a plane mirror at an angle of \(30^{\circ}\) then deviation produced by a plane mirror is (A) \(60^{\circ}\) (B) \(90^{\circ}\) (C) \(120^{\circ}\) (D) \(150^{\circ}\)

Short Answer

Expert verified
The deviation produced by a plane mirror when a ray of light is incident at an angle of \(30^{\circ}\) is \(60^{\circ}\). This is calculated using the law of reflection, where the angle of incidence is equal to the angle of reflection. In this case, both angles are \(30^{\circ}\), so the total deviation is \(30^{\circ} + 30^{\circ} = 60^{\circ}\).

Step by step solution

01

Identify the Law of Reflection

According to the law of reflection, the angle of incidence (i) is equal to the angle of reflection (r), which can be represented mathematically as: \(i = r\)
02

Calculate the angle of reflection

As given in the problem, the angle of incidence (i) is \(30^{\circ}\). We can use the law of reflection to find the angle of reflection (r). \(i = r\) \Rightarrow \(30^{\circ} = r\) So, the angle of reflection is also \(30^{\circ}\).
03

Calculate the deviation produced by the mirror

Deviation (D) produced by a plane mirror can be calculated as the difference between the angle of incidence (i) and the angle of reflection (r). In this case, it is the sum of the two angles, since both angles are on the same side of the normal line. \(D = i + r\) \Rightarrow \(D = 30^{\circ} + 30^{\circ}\) \Rightarrow \(D = 60^{\circ}\) Thus, the deviation produced by a plane mirror is \(60^{\circ}\), which corresponds to the option (A) in the given exercise.

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Most popular questions from this chapter

The fringe width for red $\beta_{\mathrm{r}}\left(\lambda_{\mathrm{T}}=8000 \AA\right.$ ) and the fringe width for violet \(\beta_{\mathrm{v}}\left(\lambda_{\mathrm{v}}=4000 \AA\right.\) ) then \(\left(\beta_{\mathrm{r}} / \beta_{\mathrm{v}}\right)=\) (A) \(2: 1\) (B) \(1: 2\) (C) \(1: 1\) (D) \(\sqrt{2}: 1\)

To get five images of a single object one should have two plane mirrors at an angle of (A) \(36^{\circ}\) (B) \(72^{\circ}\) (C) \(80^{\circ}\) (D) \(302^{\circ}\)

If thin prism of \(5^{\circ}\) gives a deviation of \(2^{\circ}\) then the refractive index of material of prism is (A) \(1.4\) (B) \(1.5\) (C) \(1.6\) (D) \(1.0\)

A concave mirror has a focal length \(30 \mathrm{~cm}\). The distance between the two position of the object for which image size is double of the object is (A) \(30 \mathrm{~cm}\) (B) \(15 \mathrm{~cm} \quad \overline{\text { (C) }-25 \mathrm{~cm}}\) (D) \(-15 \mathrm{~cm}\)

A ray of light passes through a prism having refractive index \((\mathrm{n}=\sqrt{2})\), Suffers minimum deviation If angle of incident is double the angle of refraction within prism then angle of prism is (A) \(30^{\circ}\) (B) \(60^{\circ}\) (C) \(90^{\circ}\) (D) \(180^{\circ}\)
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