Question

find the size,nature and position of image formed when an object of size 1cm is placed at a distance of 15cm from a concave mirror of focal length 10cm.​

Answer 1

$\large\bf {\orange {\underline { \underline {Gíven}} : - }}$

• object distance,u = -15cm
• Focal length,f = -10cm
• Height of object,h = 1cm

$\large\bf {\orange {\underline { \underline {To \: fínd}} : - }}$

(i) position of the image,

(ii) Nature of the image and

(iii) Size of the image

$\large\bf {\orange {\underline { \underline {Solutíon}} : - }}$

Here, we have been given the distance and Focal length, so, first of all we will find out the image distance which will give us the position of image

(i) position of image

using Mirror formula,

$\longrightarrow \sf \frac{1}{v} + \frac{1}{u} = \frac{1}{f}$

$\longrightarrow \sf \frac{1}{v} + \frac{1}{ - 15} = \frac{1}{ - 10}$

$\longrightarrow \sf \frac{1}{v} - \frac{1}{15} = - \frac{1}{10}$

$\longrightarrow\sf \frac{1}{v} = - \frac{1}{10} + \frac{1}{15}$

$\longrightarrow \sf\frac{1}{v} = \frac{ - 3 + 2}{30}$

$\longrightarrow \sf \frac{1}{v} = - \frac{1}{30}$

$\longrightarrow \sf v = - 30cm$

Thus, the position of image is 30cm to left side of mirror or 30cm in front of mirror (minus sign show the left side of mirror)

(ii) Nature of image :-

The image is formed in front of the concave mirror

The image is "real and inverted"

(iii) Size of image :-

To find the size of image, we will have to calculate the magnification

$\longrightarrow\sf m = - \frac{v}{u}$

Here,

Image distance, v = -30cm

Object distance, u = -15cm

$\longrightarrow \sf m = - \cancel \frac{ - 30}{ - 15}$

$\longrightarrow\sf magnification \: m = - 2$

we also know another formula for magnification,

$\longrightarrow \sf m = \frac{h'}{h}$

here,

magnification, m = -2

height of object, h = 1cm

height of image, h' = ?

$\longrightarrow \sf - 2 = \frac{h'}{1}$

$\longrightarrow \sf height \: of \: image \: h' = - 2 \times 1 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf= - 2cm$

Thus, the size of image is 2cm long.