Question

An object 4 cm in height is placed at 15 cm in front of a concave mirror of focal length 10 cm. at what distance from the mirror should a screen be placed to obtain a sharp image of the object. Calculate the height of image.

Answer 1

The height of image is 30 cm.

Explanation:

The "u" distance of the image is given as -15 cm while the focal length of the object is given is -10 CM.

Now putting these values in the lens formula we can get the distance of the image formed

$\frac{1}{v} + \frac{1}{u} = \frac{1}{f} \rightarrow \frac{1}{v} = \frac{1}{15} - \frac{1}{10}$

⇒ v = -30 cm

After knowing the distance of object to be placed let us see the formula for magnification given by $-\frac{v}{u}$.

On applying the value we get,

m =$\frac{h'}{h}$ = $- \frac{-30}{-15}$

⇒ h’ = $-30 \times \frac{4}{15}$ = -8cm

for the purpose of getting an image that is sharp it should be placed at 30 cm.

To know more:

Object of height 8cm is placed at 50 cm in front of a concave mirror of focal length 30 . At what distance from mirror should a screen be placed in order to obtain a sharp image ? Also find the nature and size of image

https://brainly.in/question/10388829

Answer 2

Answer:

Explanation:

Given :-

f = - 10 cm

u = - 15 cm

h₂ = 4 cm

Solution :-

Using the mirror formula,

1/f = 1/v + 1/u

⇒ 1/v + 1/-15 = 1/- 10

⇒ 1/v = 1/- 10 + 1/15

⇒ 1/v = (- 15 + 10)/150

⇒ 1/v = - 5/150

⇒ v = - 30 cm

Thus, to obtain a sharp image of the object the screen should be placed in front of the mirror at a distance of 30 cm from the mirror.

Magnification, m = - v/u = h₁/h₂

⇒ m = - 30/- 15

⇒ m = - 2

⇒ h₁ = - 8 cm

Hence, the image height will be 8 cm.