Question

a concave mirror has focal length 20cm and object at a distance of 16 cm from it. what is the distance of the image​

Answer 1

Answer:

• position of image will be 80 cm behind the mirror.

Explanation:

Given that,

• focal length of concave mirror, f = -20 cm
• position of object, u = -16 cm

we need to find

• position of image, v = ?

Using mirror formula

→ 1/f = 1/v + 1/u

→ 1/(-20) = 1/v  + 1/(-16)

→ 1/(-20) = 1/v + 1/(-16)

→ 1/v = 1/(-20) + 1/16

→ 1/v = ( -4 + 5 ) / 80

→ 1/v = 1 / 80

→ v = 80 cm

therefore,

position of image will be 80 cm behind the mirror.

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Distance\:of\:the\:image=80\:cm}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Focal \: length(f) = -20 \: cm \\ \\ \tt: \implies Object \: distance(u) = 16 \: cm \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Image \: Distance(v) = ?$

• According to given question :

$\tt\circ\:In\:concave\:mirror\:focal\:length\:is\:negative\\\\ \bold{As \: we \: know \: that} \\ \tt: \implies \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \\ \\ \tt: \implies \frac{1}{-20} = \frac{1}{v} + \frac{1}{16} \\ \\ \tt: \implies \frac{1}{-20} - \frac{1}{16} = \frac{1}{v} \\\\ \tt:\implies \frac{-1}{20}-\frac{1}{16}=\frac{1}{v}\\\\ \tt:\implies \frac{-(4-5)}{20} =\frac{1}{v}\\\\ \tt: \implies \frac{-4+ 5}{80} = \frac{1}{v} \\ \\ \tt: \implies \frac{ 1}{80} = \frac{1}{v} \\ \\ \green{\tt: \implies v = 80 \: cm} \\ \\ \green{\tt \therefore Image\:distance \: is \: 80 \: cm}$