A light bulb is placed 17.1 cm in front of a concave mirror. When the concave mirror is replaced by a plane mirror in the same location, the bulb's image moves 6.60 cm closer to the mirror. Calculate the focal length of the concave mirror.

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To solve this problem, we can use the mirror equation:

1/f = 1/di + 1/do

where:
- f is the focal length of the mirror
- di is the image distance from the mirror
- do is the object distance from the mirror

Let's first calculate the object distance (do) for the concave mirror. The object distance for a plane mirror is equal to the distance between the object and the mirror, which is given as 17.1 cm.

do = 17.1 cm

Now, let's calculate the image distance (di) when the concave mirror is replaced by a plane mirror. We know that the image moves 6.60 cm closer to the mirror, so we can subtract this distance from the original object distance.

di = do - 6.60 cm
di = 17.1 cm - 6.60 cm
di = 10.5 cm

Now, let's substitute the values of di and do into the mirror equation and solve for f:

1/f = 1/di + 1/do
1/f = 1/10.5 cm + 1/17.1 cm

To add these fractions, we need a common denominator. The common denominator for 10.5 and 17.1 is 180.6. So, let's rewrite the equation with the common denominator:

1/f = (1 * 17.1 + 1 * 10.5) / (10.5 * 17.1)
1/f = (17.1 + 10.5) / 180.6
1/f = 27.6 / 180.6

Now, let's divide 27.6 by 180.6 to calculate 1/f:

1/f ≈ 0.1526

To get the focal length (f), we can take the reciprocal of 1/f:

f ≈ 1/0.1526
f ≈ 6.54 cm

Therefore, the focal length of the concave mirror is approximately 6.54 cm.