Question

An object 3cm in size,is placed at 20cm in front of a concave mirror of focal length 12 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image. also find the nature and size of the image.find

Answer 1

Ho = 3cm
U = -20 [sign convention]
F = -12. [sign convention]
V = ?
Using Mirror formula,
1/f = 1/U+1/V
1/V = 1/U-1/F
1/V = 1/(-20)-1/(-12)
1/V = 1/(-20)+1/12
1/V = 1/20-1/12
1/V = 3-5/60
1/V = -2/60 = -1/30
V = -30
We know that,
M = -V/U= Hi/Ho. [where Hi is height of Image and Ho is height of object]
-V/U = Hi/Ho
-(-30)/(-20) = Hi/3
30/-20 = Hi/3
-20 Hi = 30×3
Hi = 90/-20
Hi =- 4.5
M is negative , So image is Inverted and real.

Answer 2

HEYA FRND..........☺

hₒ = 3 cm

u = - 20 cm

f = - 12 cm

v = ?

Mirror formula :-

$\frac{1}{v} \: + \: \frac{1}{u} \: = \: \frac{1}{f}$

$\frac{1}{v} \: = \: \frac{1}{f} \: - \: \frac{1}{u}$

$\frac{1}{v} = \frac{1}{ - 12} - ( \frac{1}{ - 20} )$

$= > \: \frac{1}{v} = \: \frac{ - 1}{12} \: + \: \frac{1}{20}$

$= > \: \frac{1}{v} \: = \: \frac{ - 5 + 3}{60}$

$= > \: v \: = \: \frac{60}{ - 2}$

$= > \: v \: = \: - 30cm$

So, The screen should be placed at 30cm from the mirror.

____________

Now,

Since v is '-ve' , the nature of image is Virtual & Erect.

And,

hᵢ/hₒ = -v/u

So,

hᵢ = - v × hₒ / u

hᵢ = -30 × 3/20

hᵢ = -90/20

hᵢ = - 4.5 cm

So,

Size of image is bigger.

______$ANS$

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Hope It Will Help U ..........^_^