Question

3. An object is placed at a distance of 10 cm from a convex mirror of focal length 20 cm. Find
the position and nature of image.

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Answer 1

$\red{\bf {Question}}$

An object is placed at a distance of 10cm. from a convex mirror of focal length 20cm. Find the position and nature of the image.

$\green{\bf {Answer}}$

$\underline{\boxed{\sf\purple{u = 10cm}}}$

(because object is in front of the mirror)

$\underline{\boxed{\sf\purple{f = 20cm}}}$

$\begin{gathered}\color{red}Using \:Mirror \: formula:- \\ \\ \color{magenta}\frac{1}{f} = \frac{1}{v} + \frac{1}{u}\\ \\ \color{green}↦\frac{1}{20 } = \frac{1}{v} + (\frac{1}{ - 10} ) \\ \\ \color{maroon}↦ \frac{1}{20 } = \frac{1}{v} - \frac{1}{ 10} \\ \\ \color{gold}↦\frac{1}{20 } + \frac{1}{10} = \frac{1}{v} \\ \\\color{violet}↦ \frac{1 + 2}{20} = \frac{3}{20} \\ \\ \color{darkblue}↦v = \frac{20}{3} \color{purple}=6.67cm \end{gathered}$

Position of image(v) = 6.67cm in front of mirror

Nature of image = virtual, erect and diminished

(because it is a convex mirror which makes virtual,erect

and diminished image in all positions of the object)

Thankyou :)

Answer 2

Answer:

Hence the image will be formed on the left side of the lens (shown by negative sign) at a distance of 20 cm. Also we can see that the object is in between the lens and image, hence the image is virtual. As both the object and image is above the principle axis, hence it is erect too.

Explanation:

An object is placed at a distance of 10cm from a convex mirror of focal length 20cm. ... Since the image is formed behind the convex mirror, therefore, the nature of image is virtual and erect

we can find the position of image by calculating the image distance, v. <br> Here, Object distcance, u = - 10 cm (To the left of mirror) <br> Image distance, v = ? (To be calculated ) <br> And, Focal length, f = + 15 cm (It is a convex mirror) <br> Putting these values in the mirror formula : < So, Image distance, v = + 6 cm <br> Thus, the position of image is at a distance of 6 cm from the convex mirror on its right side (behind the mirror). Since the image is formed behind the convex mirror, therefore, the nature of image is virtual and erect.