Question

A 3.0 cm lighted candle is placed 20 cm from a concave spherical mirror with a radius of curvature of 30 cm.(a)Where should a screen be placed (in cm) in order to see the candle's image clearly? (Give your answer as a distance from the center of the mirror.) cm(b)What is the minimum height (in cm) of the screen in order to see the candle's complete image? cm

Answer 1

To see the candle's image clearly, the screen should be placed at the focal point of the concave mirror, which is 15 cm from the center. The minimum height of the screen to see the candle's complete image is 30 cm.

Step-by-step explanation:

To see the image of the candle clearly, the screen should be placed at the focal point of the mirror. The focal point of a concave mirror is located at half of the radius of curvature. In this case, the radius of curvature is 30 cm, so the focal point is 15 cm from the center of the mirror.

To see the complete image of the candle, the screen should be placed at twice the distance of the focal point from the center of the mirror. This means the screen should be placed at 2 times 15 cm, which is 30 cm from the center of the mirror.

Answer 2

Given:

The object's height is h = 3 cm

The object's distance from the concave mirror is u = -20 cm

The radius of curvature is R = - 30 cm

Required:

(a) Image's distance from the mirror

(b) Image's height

Step-by-step explanation:

The focal length of the mirror can be calculated as

`\begin{gathered} f=(R)/(2) \\ =-(30)/(2) \\ =-15\text{ cm} \end{gathered}`

(a) The image's distance can be calculated using the mirror formula as

`\begin{gathered} (1)/(v)+(1)/(u)=(1)/(f) \\ (1)/(v)=(1)/(f)-(1)/(u) \\ =(1)/(-15)-(1)/(-20) \\ v=-60\text{ cm} \end{gathered}`

(b) The image's height can be calculated as

`\begin{gathered} (h^(\prime))/(h)=-(v)/(u) \\ h^(\prime)=-(v)/(u)* h \\ =(-(-60))/(-20)*3 \\ =-9\text{ cm} \end{gathered}`

Final Answer:

(a) Image's distance from the mirror is v = -60 cm

(b) Image's height is h' = -9 cm