Can a diverging lens be used as a magnifying glass? Explain. (Select all that ap

Question

Can a diverging lens be used as a magnifying glass? Explain. (Select all that apply.) Yes, when it causes rays to converge so that the rays traced backward form a larger image. Yes, by holding it close to the object so that the rays on the backside of the lens converge. No. The diverging rays always lead to an image smaller than the object. Yes, by holding it far from the object so that the rays on the backside of the lens converge. Use the worked example above to help you solve this problem. A diverging lens of focal length f = -8.7 cm forms images of an object situated at various distances. (a) If the object is placed p_1 = 26.1 cm from the lens, locate the image, state whether it's real or virtual, and find its magnification. (b) Repeat the problem when the object is at p_2 = 8.7 cm. (c) Repeat the problem again when the object is 4.35 cm from the lens. Use the values from PRACTICE IT to help you work this exercise. Repeat the calculation, finding the position of the image and the magnification if the object is 17.9 cm from the lens.

Explanation / Answer

here f = - 8.7 cm = - 0.087 m

(a) when u = 26.1 cm

then from lens eqution

- 1 / u + 1 / f = 1 / v

- 1 / ( 0.261) + 1 / (- 0.087 ) = 1 / v

1 / v = (-15.3256)

v = - 0.06525 m = - 6.525 cm Ans

so the image is virtual and its magnification

m = - v/u

= - (- 0.06525) / ( 0.261 ) = 0.25 Ans

(b) when u = 8.7 cm = 0.087 m

then - 1 / ( 0.087) + 1 / ( - 0.087 ) = 1 / v

1 / v = - 22.9885

v = - 0.0435 m = - 4.35 cm Ans

so the image will virtual and magnification

m = - v/u

= - (- 4.35) / ( 8.7) = 0.5 Ans

(c) when u = 4.35 cm = 0.0435 m

then   

- 1 / 0.0435 + 1 / ( -0.087 ) = 1/ v

1 / v = - 34.4827

v = - 0.029 m = - 2.9 cm Ans

so the image is virtual and magnifiation

m = - v/u

= - (- 2.9) / (4.35) = 0.667 Ans

(d) when u = 17.9 cm = 0.179 m

then

- 1 / 0.179 + 1 / ( - 0.087 ) = 1 / v

1 / v = - 17.0808

v = - 0.0585 m = - 5.85 cm

so the image will virtual and magnification

m = - v /u

= - (- 5.85) / 17.9 = 0.326 Ans

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