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kakasveta [241]
3 years ago
12

Example: What power of spectacle lens is needed to correct the vision of a nearsighted person

Physics
1 answer:
Aleksandr [31]3 years ago
4 0
<h3>Concave or diverging lens is needed correct the vision of a nearsighted person  whose far point is 30.0 cm</h3>

<em><u>Solution:</u></em>

Nearsighted person will not be able to see the distant objects clearly

Now, we want the near sighted person to see the distant objects clearly

<em><u>The lens equation is given as:</u></em>

P = \frac{1}{d_o} + \frac{1}{d_i}

For distant vision, d_0 = \infty

d_i = image\ distance\\\\d_0 = lens\ to\ retina\ distance

The image of 30 cm from eye will be 28.5 cm to left of spectacle lens

Therefore,

d_i = -28.5\ cm = 0.285\ meter

From lens equation,

P = \frac{1}{ \infty } + \frac{1}{-0.285\ meter}\\\\P = 0 - 3.51 \\\\P = -3.51\ diopter

The negative power -3.51 D denotes that a concave or diverging lens is needed

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A 1000 kg satellite and a 2000 kg satellite follow exactly the same orbit around the earth. What is the ratio F1/F2 of the gravi
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Answer:

the <em>ratio F1/F2 = 1/2</em>

the <em>ratio a1/a2 = 1</em>

Explanation:

The force that both satellites experience is:

F1 = G M_e m1 / r²       and

F2 = G M_e m2 / r²

where

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  • m2 is the mass of satellite 2
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Therefore,

F1/F2 = [G M_e m1 / r²] / [G M_e m2 / r²]

F1/F2 = [G M_e m1 / r²] × [r² / G M_e m2]

F1/F2 = m1/m2

F1/F2 = 1000/2000

<em>F1/F2 = 1/2</em>

The other force that the two satellites experience is the centripetal force. Therefore,

F1c = m1 v² / r    and

F2c = m2 v² / r

where

  • m1 is the mass of satellite 1
  • m2 is the mass of satellite 2
  • v is the orbital velocity
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Thus,

a1 = v² / r ⇒ v² = r a1    and

a2 = v² / r ⇒ v² = r a2

Therefore,

F1c = m1 a1 r / r = m1 a1

F2c = m2 a2 r / r = m2 a2

In order for the satellites to stay in orbit, the gravitational force must equal the centripetal force. Thus,

F1 = F1c

G M_e m1 / r² = m1 a1

a1 = G M_e / r²

also

a2 = G M_e / r²

Thus,

a1/a2 = [G M_e / r²] / [G M_e / r²]

<em>a1/a2 = 1</em>

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