Why do we prefer a convex mirror as a rear-view mirror in vehicles?

Uses of convex mirrors: Drivers use convex mirror as a rear-view mirror in automobiles because of the following two reasons:

1. A convex mirror always forms an erect, virtual and diminished image of an object placed anywhere in front of it.

2. A convex mirror has a wider field of view than a plane mirror of the same size, as shown in Fig.

Thus convex mirrors enable the driver to view much larger traffic behind him than would be possible with a plane mirror. The main disadvantage of a convex mirror is that it does not give the correct distance and the speed of the vehicle approaching from behind.

Fig. Field of view of (a) a plane mirror (b) a convex mirror

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Define the principal focus of a concave mirror.

Principal focus is that point on the principal axis at which, a beam of light which is incident parallel to the principal axis converges after reflection from the concave mirror.

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A concave lens of focal length 15 cm forms an image 10 cm from the lens. How far is the object placed from the lens? Draw the ray diagram.

Focal length, f = - 15 cm [f is - ve for a concave lens]

Image distance, v = - 10 cm [Concave lens forms virtual image on same side as the object, so v is - ve]

As,

Object distance, u = -30 cm. Ans.

Drawing the ray diagram: Using a scale of 1: 5, we get v = - 2 cm, f = - 3 cm. We draw the ray diagram as follows:

(i) Draw the principal axis (a horizontal line).

(ii) Draw a convex lens, keeping principal centre (C) on the principal axis.

(iii) Mark points F and B on the left side of lens at a distance of 3 cm and 2 cm respectively.

(iv) Join any point D (nearly at the top of lens) and F by a dotted line.

(v) Draw a line AD, parallel to principal axis.

(vi) Draw a line A'B', perpendicular to principal axis from B'.

(vii) Draw a line CA', backwards, so that it meets the line from D parallel to principal axis at A.

(viii) Draw a line AB, perpendicular (downwards) from A to meet the principal axis at B.

(ix) The AB is position of object. Measure distance BC. It will be found to be equal to 6 cm.

Thus, object is placed at a distance of 6 cm × 5 = 30 cm from the lens.

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Name a mirror that can give an erect and enlarged image of an object.

Concave mirror has the property of giving an erect and enlarged image of an object.

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The radius of curvature of a spherical mirror is 20 cm. What is its focal length?

Given,

Radius of curvature, R = 20 cm

Relationship between radius and focal length is as :

Focal length = $\frac{1}{2}\times \mathrm{Radius}\mathrm{of}\mathrm{curvature}$

$\Rightarrow $ $\mathrm{f}=\frac{20}{2}=10\mathrm{cm}$is the focal length of the mirror.

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