Question

When an object 5 cm height is placed at a distance 60 cm in front of a concave mirror of focal length 10 cm find the position and size of the image please send the correct step by step explanation​

Answer 1

Given :

In concave mirror,

Object distance = 5cm

Object distance = - 60cm

Focal lenght = - 10cm

To find :

The position and size of the image.

Solution :

In concave mirror focal length and image distance is negative.

» A formula which gives the relationship between image distance, object distance and focal length of a sperical mirror is known as the mirror formula .i.e.,

$\boxed{\bf \dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}}$

where,

• v denotes Image distance
• u denotes object distance
• f denotes focal length

now, substituting all the given values,

$\leadsto{\sf \dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f} }$

$\leadsto{\sf \dfrac{1}{v} + \dfrac{1}{ (- 60)} = \dfrac{1}{( - 10)} }$

$\leadsto{\sf \dfrac{1}{v} - \dfrac{1}{ 60} = - \dfrac{1}{10} }$

$\leadsto{\sf \dfrac{1}{v} = - \dfrac{1}{10} + \dfrac{1}{60} }$

$\leadsto{\sf \dfrac{1}{v} = \dfrac{ - 6 + 1}{60} }$

$\leadsto{\sf \dfrac{1}{v} = \dfrac{ - 5}{60} }$

$\leadsto{\sf \dfrac{1}{v} = - \dfrac{ 1}{12} }$

$\leadsto \underline{ \boxed{\sf v = - 12cm }}$

Thus, the position of image is -12cm.

» The Magnification produced by a mirror is equal to the ratio of the image distance to the object distance with a minus sign and is also equal to the ratio of height of the image to the height of the object .i.e.,

$\boxed{ \bf m = - \dfrac{v}{u} = \dfrac{h'}{h}}$

where,

• v denotes image distance
• u denotes object distance
• h' denotes image height
• h denotes object height

Now, substituting all the given values in the formula,

$\leadsto{\sf -\dfrac{v}{u} = \dfrac{h'}{h}}$

$\leadsto{\sf -\dfrac{( - 12)}{( - 60)} = \dfrac{h'}{5}}$

$\leadsto{\sf -\dfrac{1}{5} = \dfrac{h'}{5}}$

$\leadsto{\sf h' = - \dfrac{5}{5} }$

$\leadsto \underline{ \boxed{\sf h' = - 1cm }}$

thus, the size of the image is -1cm.

Answer 2

Answer:

The size of the image is -1 cm