An object is placed 18 cm in front of a spherical mirror- If the images formed at 4 cm to the right of the mirror calculate its focal length- Is the mirror is concave or convex- What is the nature of the image- What is the radius of curvature -

Here object distance (u) = 18 cm and image distance(v)= 4 cm since the image is formed at right side so it is a virtual and erect image. generally, convex mirro ...

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Standard X

Physics

Image Formation by Spherical Mirrors

An object is ...

Question

An object is placed 18 cm in front of a spherical mirror. If the image is formed at 4 cm to the right of the mirror then calculate its focal length. Is the mirror concave or convex. What is the nature of the image. What is the radius of curvature?

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Solution

Step 1: Given Data
Since the image is formed at right side so it is a virtual and erect image. Generally, convex mirror forms virtual and erect image. So it is a convex mirror.
Object distance $u = - 18 c m$
Image distance, $v = 4 c m$

Step 2: Calculation of focal length

According to the mirror formula,
$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$
$\frac{1}{f} = \frac{1}{4} + \frac{1}{- 18}$
$\frac{1}{f} = \frac{9 - 2}{36}$
$f = \frac{36}{7}$
$f = 5.1 c m$

The radius of curvature is $2 f$ =2 $\times$ $5.1 = 10.2 c m$

Focal lenght $= 5.1 c m$ and radius of curvature $= 10.2 c m$

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