Math, asked by vaishnavitiwari1041, 1 year ago

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Answered by hereisayushh02

$\huge\underline\mathfrak\red{Explanation\: ↑}$

*next que is almost same as previous que( can take help of this solution ).

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Answered by ItSdHrUvSiNgH

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Let...

h1 be height of object.. = 4 cm

u be distance from lens = 15 cm

Power = -10 D

[Here -ve sign of power which is because it's a concave lens]

$ \implies P = \frac{1}{f} \\ \implies f = \frac{1}{P} \\ \implies f = - \frac{1}{10} \\ \implies f = - 0.1cm$

So, According to lens formula..

$\implies \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \\ \implies \frac{1}{v} = \frac{1}{f} - \frac{1}{u} \\ \implies \frac{1}{v} = - \frac{1}{0.1} + \frac{1}{15 } \\ \implies \frac{1}{v} = \frac{14.9}{1.5} \\ \implies v \approx 0.01 \\$

$ \implies magnification = - \frac{v}{u} \\ \implies m = \dfrac{\cancel{ 0.01} }{\cancel{15}} \\ \implies \: m = 0.0006 \\ \:$

From here,

We are clear that=>

Image is diminished..

$ \implies m = \frac{h2}{h1} \\ \implies 0.0006 = \frac{h2}{4} \\ \implies h2 = 0.0024$

So size of image is 0.0024 cm.

24]

height of object (h1) = 4.25 mm

= 0.425 cm

u = distance from lens = -10 cm

P = +5D

[Here +ve sign of power which is because it's a convex lens]

$ \implies \frac{1}{f} = p \\ \implies f = \frac{1}{p} \\ \implies f = \frac{1}{5} = 0.25 \: cm$

By lens formula..

$\implies \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \\ \implies \frac{1}{v} = \frac{1}{f} - \frac{1}{u} \\ \implies \frac{1}{v} = \frac{1}{0.25} + \frac{1}{10} \\ \implies \frac{1}{v} = 5 + \frac{1}{10} \\ \implies \frac{1}{v} = \dfrac{\cancel 51}{\cancel 10} \\ \implies v = 0.196 \: cm$

$\implies m = \frac{ - v}{u} \\ \implies m = \frac{\cancel {0.196}}{ \cancel {10}} \\ \implies m = 0.0196$

Here,

Here, it is clear that image is diminished

$ \implies magnification = \frac{h2}{h1} \\ \implies 0.0196 = \frac{h2}{0.425} \\ \implies h2 = 0.0083 \: cm$

So, size of image is 0.0083 cm.

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