A 5.00 cm tall candle is placed at a distance of 50.0 cm from a double convex lens having a focal length of 15.0 cm. What is the image distance?



-21.4 cm

21.4 cm

65 cm

35 cm

Review and use the lens equation.

1/do + 1/di = 1/f

Candle height does not affect image position. Let x be the image location

1/50 + 1/x = 1/f = 1/15

1/x = 10/150 - 3/150 = 7/150
x = 150/7 = (one of your choices)

To find the image distance, we can use the lens formula:

1/f = 1/v - 1/u

Where:
f = focal length of the lens
v = image distance
u = object distance

Given:
f = 15.0 cm
u = -50.0 cm (negative because the object is placed on the opposite side of the lens)

Plugging these values into the equation, we can solve for v:

1/15.0 = 1/v - 1/-50.0

Now, simplify the equation:

1/15.0 = (50.0 - v) / (-50.0v)

To simplify further, cross-multiply:

(-1v) /15.0 = (50.0 - v)

Multiply both sides by 15.0 to eliminate the fraction:

-1v = 750 - 15v

Simplify further:

14v = 750

Divide both sides by 14:

v = 750 / 14

v ≈ 53.571 cm

Therefore, the image distance is approximately 53.571 cm. However, since our object distance (u) is negative, the image distance (v) should also be negative. So, the correct answer is -53.571 cm, which when rounded is approximately -53.6 cm.

Therefore, the image distance is approximately -53.6 cm.