Question

You hold a spherical salad bowl 90 cm in front of your face with the bottom of the bowl
facing you. The salad bowl is made of polished metal with a 35-cm radius of curvature. (a)
Where is the image of your 2.0-cm-tall nose located? (b) What are the image’s size, orientation,
and nature (real or virtual)?

Answer 1

Answer to Question #78532, Physics / Electromagnetism

You hold a spherical salad bowl $90~\mathrm{cm}$ in front of your face with the bottom of the bowl facing you. The salad bowl is made of polished metal with a $35~\mathrm{cm}$ radius of curvature.

(a) Where is the image of your $2.0~\mathrm{cm}$ tall nose located?

Answer:

(b) What are the image's size, orientation, and nature (real or virtual)?

Solution.

$$\frac{1}{u} - \frac{1}{v} = -\frac{2}{R}$$ $$R = 35~\mathrm{cm}; u = 2~\mathrm{cm}$$

$v$ is size of image

$$v = \frac{uR}{R + 2u} = \frac{2 \cdot 35}{35 + 2 \cdot 2} = \frac{70}{39}~\mathrm{cm}$$

Orientation of image: vertical

Since the nose is located at the distance from the bowl which is more than focus, then the image is real:

$$\text{focus: } f = \frac{R}{2} = \frac{35}{2} = 17.5~\mathrm{cm}$$ $$f < 90~\mathrm{cm}$$

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