Physics
Physics
5th Edition
ISBN: 9781260486919
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 24, Problem 30P

(a)

To determine

The refractive power of the corrective eyeglass lens to enable the man to clearly see distant objects.

(a)

Expert Solution
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Answer to Problem 30P

The refractive power of the corrective eyeglass lens to enable the man to clearly see distant objects is 0.51 D.

Explanation of Solution

Refractive power of a lens is the reciprocal of its focal length.

  P=1f                                                                                                                      (I)

Here, P is the refractive power of the lens and f is the focal length of the lens.

Write the lens equation.

  1f=1p+1q                                                                                                         (II)

Here, p is the object distance and q is the image distance

Put equation (II) in equation (I).

  P=1p+1q                                                                                                              (III)

Conclusion:

To clear distant objects, the object distance of the lens should be infinity.

Given that the man cannot see objects farther than 2.0 m away and the distance between the eyes and the lens is 2.0 cm .

Find the image distance of the lens.

  q=2.0 m+2.0 cm(1 m100 cm)=2.0 m+0.020 m=2.02 m

Substitute  for p and 2.02 m for q in equation (III) to find P .

  P=1+12.02 m=0.505 D0.51 D

Therefore, the refractive power of the corrective eyeglass lens to enable the man to clearly see distant objects is 0.51 D.

(b)

To determine

The near point of the man can see clearly with and without his glasses.

(b)

Expert Solution
Check Mark

Answer to Problem 30P

The near point of the man with his glasses is 25 cm and without his glasses is 22 cm .

Explanation of Solution

Use equation (III) to find the refractive power of eye.

  Peye=1p+1q

Here, Peye is the refractive power of the eye.

Substitute 2.0 m for p and 2.0 cm for q in the above equation to find Peye .

  Peye=12.0 m+12.0 cm(1 m100 cm)=12.0 m+10.020 m=50.5 D

It is given that the power of accommodation of the eye is 4.0 D .

Find the refractive power of the eye using the accommodation.

  Peye=50.5 D+4.0 D=54.5 D

Here, Peye is the refractive power of the eye using the accommodation.

Rewrite equation (I) for p .

  p=(1f1q)1

Put equation (I) in the above equation.

  p=(P1q)1                                                                                                       (IV)

Replace P in equation (IV) by Peye to find the expression for the near point without glasses.

  p=(Peye1q)1                                                                                                       (V)

Write the equation for the refractive power of the eye with the glasses.

  Peg=Peye+Pglasses

Here, Peg is the refractive power of the eye with the glasses and Pglasses is the refractive power of the glasses.

Substitute 50.5 D for Peye and 0.505 D for Pglasses in the above equation to find Peg .

  Peg=50.5 D+(0.505 D)=50 D

Find the refractive power of the eye with the glasses using the accommodation.

  Peg=50 D+4.0 D=54 D

Here, Peg is the refractive power of the eye with the glasses using the accommodation.

Replace P in equation (IV) by Peg to find the expression for the near point with glasses.

  p=(Peg1q)1                                                                                                   (VI)

Conclusion:

Substitute 54.5 m1 for Peye and 2.0 cm for q in equation (V) to find the near point of the man without glasses.

  p=(54.5 m11 m100 cm12.0 cm)1=22 cm

Substitute 54 m1 for Peg and 2.0 cm for q in equation (VI) to find the near point of the man with glasses.

  p=(54 m11 m100 cm12.0 cm)1=25 cm

Therefore, the near point of the man with his glasses is 25 cm and without his glasses is 22 cm .

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Chapter 24 Solutions

Physics

Ch. 24.5 - Prob. 24.7PPCh. 24.6 - Prob. 24.6CPCh. 24.6 - Prob. 24.8PPCh. 24 - Prob. 1CQCh. 24 - Prob. 2CQCh. 24 - Prob. 3CQCh. 24 - Prob. 4CQCh. 24 - Prob. 5CQCh. 24 - Prob. 6CQCh. 24 - Prob. 7CQCh. 24 - Prob. 8CQCh. 24 - Prob. 9CQCh. 24 - 10. For human eyes, about 70% of the refraction...Ch. 24 - Prob. 11CQCh. 24 - Prob. 12CQCh. 24 - Prob. 13CQCh. 24 - Prob. 14CQCh. 24 - Prob. 15CQCh. 24 - Prob. 16CQCh. 24 - Prob. 17CQCh. 24 - Prob. 18CQCh. 24 - Prob. 19CQCh. 24 - Prob. 1MCQCh. 24 - Prob. 2MCQCh. 24 - Prob. 3MCQCh. 24 - Prob. 4MCQCh. 24 - Prob. 5MCQCh. 24 - Prob. 6MCQCh. 24 - Prob. 7MCQCh. 24 - Prob. 8MCQCh. 24 - Prob. 9MCQCh. 24 - Prob. 10MCQCh. 24 - Prob. 1PCh. 24 - Prob. 2PCh. 24 - Prob. 3PCh. 24 - Prob. 4PCh. 24 - Prob. 5PCh. 24 - Prob. 6PCh. 24 - Prob. 7PCh. 24 - Prob. 8PCh. 24 - Prob. 9PCh. 24 - Prob. 10PCh. 24 - Prob. 11PCh. 24 - Prob. 12PCh. 24 - Prob. 13PCh. 24 - Prob. 14PCh. 24 - Prob. 15PCh. 24 - Prob. 16PCh. 24 - Prob. 17PCh. 24 - Prob. 18PCh. 24 - Prob. 19PCh. 24 - Prob. 20PCh. 24 - Prob. 21PCh. 24 - Prob. 22PCh. 24 - Prob. 23PCh. 24 - Prob. 24PCh. 24 - Prob. 25PCh. 24 - Prob. 26PCh. 24 - Prob. 27PCh. 24 - Prob. 28PCh. 24 - Prob. 29PCh. 24 - Prob. 30PCh. 24 - 31. Suppose the distance from the lens to the...Ch. 24 - 32. ✦ Veronique is nearsighted; she cannot see...Ch. 24 - Prob. 33PCh. 24 - Prob. 35PCh. 24 - Prob. 37PCh. 24 - Prob. 36PCh. 24 - Prob. 38PCh. 24 - Prob. 34PCh. 24 - Prob. 39PCh. 24 - Prob. 40PCh. 24 - Prob. 41PCh. 24 - Prob. 42PCh. 24 - Prob. 43PCh. 24 - Prob. 44PCh. 24 - Prob. 45PCh. 24 - Prob. 46PCh. 24 - Prob. 47PCh. 24 - Prob. 48PCh. 24 - Prob. 49PCh. 24 - Prob. 50PCh. 24 - Prob. 51PCh. 24 - Prob. 52PCh. 24 - Prob. 53PCh. 24 - Prob. 54PCh. 24 - Prob. 55PCh. 24 - Prob. 56PCh. 24 - Prob. 57PCh. 24 - Prob. 58PCh. 24 - Prob. 59PCh. 24 - Prob. 61PCh. 24 - Prob. 60PCh. 24 - 62. ✦ The eyepiece of a Galilean telescope is a...Ch. 24 - Prob. 63PCh. 24 - Prob. 64PCh. 24 - Prob. 65PCh. 24 - Prob. 66PCh. 24 - Prob. 67PCh. 24 - Prob. 68PCh. 24 - Prob. 69PCh. 24 - Prob. 70PCh. 24 - Prob. 71PCh. 24 - Prob. 72PCh. 24 - Prob. 73PCh. 24 - Prob. 74PCh. 24 - Prob. 75PCh. 24 - Prob. 76PCh. 24 - Prob. 77PCh. 24 - Prob. 78PCh. 24 - Prob. 79PCh. 24 - Prob. 80PCh. 24 - Prob. 81PCh. 24 - Prob. 82PCh. 24 - Prob. 83PCh. 24 - Prob. 84PCh. 24 - Prob. 85PCh. 24 - 86. (a) What is the angular size of the Moon as...Ch. 24 - Prob. 86P
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