Question

Q. A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it. Where is the needle placed in front of the convex lens if the image is equal to the size of the object? Also, find the power of the lens.

No Spamming..!!​

Answer 1

Answer:

For convex lens,   h1 /h2  = -v/u

1 = -v/u

u= -v

According to the question,  

Using lens formula - 1/50  - 1/50  = 1/f

-2/50 =f

∴f=−25cm

there are  2 answers for this question

Object distance, u= – 50 cm

Image distance, v= 50 cm

Focal length = f

According to the lens formula,

u = -50 cm v = + 50 cm. f =? 1/f = 1/v €“ 1/u 1/f = 1/50 + 1/50 f = + 25 cm. = 0.25 m Power of lens (P) = 1/f = 1/ 0.25 = + 4D.

Answer 2

$\fcolorbox{purple}{aqu}{Solution:}$

⠀ ⠀⠀ ⠀ ⠀⠀ ⠀

$\tt{v \:=\: +50 \:cm,\: u=?, \:P = ?}$

$\tt{As\: image\: formed \:by \:lens\: is \:real, }$$\tt{inverted\: of\: the \:same\: size,\: implies }$$\tt{object \:is \:at \:2F.\: So}$$\tt{ image\: is \:at\: 2F.}$

↦$\tt{u\: =\: 2}$

↦$\tt{F \:= \:50\: cm}$

↦$\tt{f \:=}$$\tt\frac{ 50}{2 }= \:25\: cm$

↦$\tt{P\:=}$$\tt\frac{1}{f(m)}$$\tt{or}$$\tt\frac{100}{f(cm)}$

↦$\tt{P\:=}$$\tt\frac{100}{25}$$\tt{=\:4D}$

⠀ ⠀⠀ ⠀ ⠀⠀ ⠀

⠀ ⠀⠀ ⠀ ⠀⠀ ⠀

⠀ ⠀⠀ ⠀ ⠀⠀ ⠀

⠀ ⠀⠀ ⠀ ⠀⠀ ⠀

$\mathtt\blue{Answer\:⇝}$$\mathtt\pink{4D}$