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please whose rank is genius rank and ace rank please answer this A 4.00-cm tall light bulb is placed a distance of 40 cm from a concave mirror having a focal length of 16 cm. Determine the image distance​

Answer 1

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A shopkeeper earns a profit of Rs 2 by selling a pen and incurs a loss of 50 paise per pencil and loss of 15 paise per eraser while selling old stock. On a particular day, he earns a profit of Rs 10. If he sold 10 pens and number of pencils and erasers he sold are in the ratio 7:10, then find the number of pencils and eraser he sold that day.

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By selling a pen gain is Rs.2

and by selling a pencils, he loses 50 paise

and an eraser, he loses 15 paise

On one day, he gain =Rs.10

On that day he sold 10 pens and pencils and erasers in the ratio of 7:10

On ten pens, his gain =10×2=Rs.20

loss on pencils and erasers =Rs.20−Rs.10=Rs.10=1000 paise

Ratio in pencil and eraser =7:10

Let number of pencils =7x, then eraser =10x

7x×50+10x×15=1000

⇒350x+150x=1000

⇒500x=1000

⇒x=2

Numbe rof penciles =7×2=14

and number of erasers =10×2=20

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Answer 2

Height of object (h) = 4 cm

distance of object from mirror (u) = - 40 cm

focal length (f) = - 16 cm (because concave mirror's focus is outside the mirror)

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Using the mirror formula,

$\sf \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \\ \\ \sf = > \frac{1}{v} = \frac{1}{f} - \frac{1}{u} \\ \\ \sf= > \frac{1}{v} = \frac{1}{ - 16} - \frac{1}{ - 40} \\ \\ = > \sf \frac{1}{v} = \frac{ - 1}{16} + \frac{1}{40} \\ \\ \sf = > \frac{1}{v} = \frac{ - 5 + 2}{80} \\ \\ \sf = > \frac{1}{v} = \frac{ - 3}{80} \\ \\ = > \sf \: v = \frac{80}{ - 3} \\ \\ \sf= > v = - 26.66$

Hence the image distance will be 26.66 cm. image will be real and Reverse.

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Advanced calculation -

magnification,

$\sf m = - \frac{v}{u} \\ \\ \sf = - \frac{ - 26.66}{ - 40} \\ \\ \sf = - \frac{26.66}{40} \\ \\ \sf = - 0.66$

Hence the magnification is 0.66 and reverse, real.

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To find the height of image (h')

$\sf \: m = \frac{h' }{h} = - \frac{v}{u} \\ \\ \sf = > h' = - \frac{vh}{u} \\ \\ \sf= > h' = - \frac{ - 26.66 \times 4}{ - 40} \\ \\ = \sf > h' = \frac{ - 26.66}{10} \\ \\ \sf = > h' = - 2.66$

Hence height of image = 2.66 cm, it will be reverse.

hope it helps.