Answer to Question #282133 in Physics for Ella

Question

8 A pencil 10 cm long is placed 70 cm in front of a lens of focal length +50 cm. The image is ________

A. 4 cm long and upright

B. 4 cm lang and inverted

C. 25 cm long and upright

D. 25 cm long and inverted

9. The lens of the eye forms an image on the relina that is _______

A. Real and upright

B. Real and inverted

C. Virtual and upright

D. Virtual and inverted

10. Joy is farsighted. She cannot clearly see objects closer than 60 cm. Determine the lens power (reading glasses) which will help her read a magazine at a distance of 25 cm. Assume the lens is very close to the eye.

A. +2:33 D

B. -2.33 D.

C. +5.55 D

D. -5.55 D

Answer 1

8) Let's first find the image distance from the lens equation:

$$\dfrac{1}{d_o}+\dfrac{1}{d_i}=\dfrac{1}{f},$$ $$d_i=\dfrac{1}{\dfrac{1}{f}-\dfrac{1}{d_o}},$$ $$d_i=\dfrac{1}{\dfrac{1}{50\ cm}-\dfrac{1}{70\ cm}}=175\ cm.$$

Let's apply the magnification equation and find the magnification of the lens and height of the image:

$$M=-\dfrac{d_i}{d_o}=-\dfrac{175\ cm}{70\ cm}=-2.5,$$ $$M=\dfrac{h_i}{h_o},$$ $$h_i=Mh_o=-2.5\times10\ cm=-25\ cm.$$

The image is inverted and 25 cm long. Therefore, the correct answer is (D).

Answer:

D. 25 cm long and inverted

9) The lens of the eye forms an image on the retina that is real and inverted. Therefore, the correct answer is (B).

Answer:

B. Real and inverted

10)

$$P=\dfrac{1}{f}=\dfrac{1}{d_o}+\dfrac{1}{d_i},$$ $$P=\dfrac{1}{0.25\ m}+\dfrac{1}{-0.6\ m}=+2.33\ D.$$

Answer:

A. +2.33 D