Question

If an object is placed 50 cm in front of a concave mirror of 60 cm radius, what is the image size if object size is 15cm?​

Answer 1

$\huge\mathfrak\red{❥Solution}$

In numericals of optics, you must use proper sign conversation. And proper formulae assosiated with this. Best is use convention like coordinate system.

• 1) all distances are measured from centre of mirror or lense.
• 2) Towards left the distances are negative.
• 3) towards right distances are positive.

For mirror 1/v - 1/u = 1/f

For lense 1/v + 1/u = 1/f.

In given example, f = minus 30, u = minus 50. You get v as minus 75. Minus sign of v indicates it is towards left from centre of mirror. See the photo enclosed.

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Answer 2

$\huge{Given :-}$

Object distance (u)= -50cm

Radius (R)= -60cm [•°• Concave mirror]

focal length (f)= R/2= -60/2= (-30)cm

Size of object = 15cm

$\sf \red{To \: Find :-}$

We have to find the size of image

Solution :-

Using mirror formula

$\underline{\boxed{\sf \ \red{\dfrac{1}{f}= \dfrac {1}{v}+\dfrac{1}{u}}} }$

Now , by putting these values in the formula

$\begin{lgathered}\longrightarrow\sf\ \dfrac{1}{-30}= \dfrac{1}{-50}+\dfrac{1}{v}\\ \\ \\ \longrightarrow\sf\ \dfrac{-1}{30}+\dfrac{1}{50}=\dfrac{1}{v}\\ \\ \\ \longrightarrow\sf\ \dfrac{-5+3}{150}=\dfrac{1}{v}\\ \\ \\ \longrightarrow\sf\ \dfrac{-2}{150}=\dfrac{1}{v}\\ \\ \\ \longrightarrow\sf\ v= \cancel{\dfrac{-150}{2}}\\ \\ \\ \longrightarrow\purple{\sf v= (-75)cm}\end{lgathered}$

Now we have to find the size of image

By using magnification formula

$\underline{\boxed{\sf \red{\ m= \dfrac{-v}{u}= \dfrac{h_i}{h_o}}}}$

$\begin{lgathered}\longrightarrow\sf\ \dfrac{h_i}{15}=\dfrac{\not{-}(-75)}{\not{-}50}\\ \\ \\ \longrightarrow\sf\ \dfrac{h_i}{15}=\dfrac{-(75)}{50}\\ \\ \\ \longrightarrow\sf\ \ h_i= \dfrac{-(\cancel{75}\times 15)}{\cancel{50}}\\ \\ \\ \longrightarrow\sf\ \ h_i= \dfrac{-3\times 15}{2}\\ \\ \\ \longrightarrow\sf\ \ h_i= \cancel{\dfrac{-45}{2}}\\ \\ \\ \longrightarrow\sf\ \ h_i= (-22.5)\end{lgathered}$

$\underline \purple{\bigstar{\textsf{\textbf{\ Size\ of\ image = (-22.5)cm}}}}$

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