? asked in Science & MathematicsPhysics · 9 years ago

# A candle 10.4 cm tall is located 77.0 cm from a concave mirror witha focal length of 14.2 cm.?

A candle 10.4 cm tall is located 77.0 cm from a concave mirror witha focal length of 14.2 cm.

a. Draw a ray diagram to scale, to show where the image isformed. Use a parallel ray and either a focal ray or a center of curvature ray in your diagram. Label the object (d), focus (f), center of curvature (c) and image (I)

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• Ossi G
Lv 7
9 years ago

Hello

di = distance of the image

do = distance of the object

f = focus length

set up a diagram with the mirror as the y axis, and the optical axis as the x axis.

Mark the focus and radius of curvature, which is 2*f = 28.4 cm.

Place the candle 77 cm from the mirror with the base on the x axis, upright, 10.4 cm high.

Now draw a line from the top of the candle to the center of the mirror (= origin), and let it reflect back

at the same angle of incidence.

Draw another line from the top of the candle through the point on the x axis, where the radius is marked.

This line will intersect with the first line at the top of the image candle. The image candle is about 17 cm from the mirror on the same side of the mirror as the real candle. It is real, upside down, and its size is about 2 cm as judged from the drawing.

You can calculate the image distance from the mirror by using the formula

di = do*f/(do - f) = 77*14.2/(77-14.2) = 17.4 cm

and the size of the image is Object size*di/do = 10.4*17.4/77 = 2.35 cm.

Regards