an object 3.00 cm high is placed 20.0cm from a convex mirror with a focal length of magnitude 8.00 cm. Find the position of the image. (Im using 1over20.00 + 1overQ = 1over-8.00) and the answer is q= -5.71cm. can someone tell how to do the math.. I suck at algebra
1/20 + 1/q = -1/8
1/q = -0.125 -0.050 = -0.175
q = -5.714
To solve the equation 1/20.0 + 1/Q = 1/(-8.00) for Q, we can first simplify the equation by finding a common denominator:
1/20.0 + 1/Q = 1/(-8.00)
To find the common denominator, we multiply 20.0 by -8.00:
-8.00/160.0 + 1/Q = 1/(-8.00)
Next, we can add the fractions on the left side of the equation:
(-8.00 + 160.0)/160.0 + 1/Q = 1/(-8.00)
152.0/160.0 + 1/Q = 1/(-8.00)
Simplifying this further, we can divide both the numerator and denominator of 152.0/160.0 by 8:
19.0/20.0 + 1/Q = 1/(-8.00)
Now, we can subtract 19.0/20.0 from both sides of the equation:
1/Q = (1/(-8.00)) - (19.0/20.0)
To subtract fractions, we need a common denominator. The common denominator in this case is 160:
1/Q = (-20.0/160.0) - (152.0/160.0)
Combining the numerators:
1/Q = (-20.0 - 152.0)/160.0
1/Q = -172.0/160.0
Simplifying the expression further:
1/Q = -43.0/40.0
Now, we can find the reciprocal of both sides of the equation to solve for Q:
Q/1 = -40.0/(-43.0)
Finally, we can divide -40.0 by -43.0 to get the value of Q:
Q = 40.0/43.0 ≈ 0.9302
Therefore, the position of the image is approximately Q = -5.71 cm.
Sure! I can help you with the math. The formula you mentioned, 1/f = 1/p + 1/q, is called the mirror equation. In this equation, f represents the focal length, p represents the object distance, and q represents the image distance.
Given:
f = -8.00 cm (negative because it's a convex mirror)
p = 20.0 cm
To find the position of the image (q), we can rearrange the equation as follows:
1/f = 1/p + 1/q
First, let's substitute the known values into the equation:
1/-8.00 = 1/20.0 + 1/q
Next, let's simplify the equation by finding the common denominator:
-1/8.00 = (1 + 20.0/q)
To eliminate the fraction, we can multiply both sides of the equation by -8.00:
-8.00 * (-1/8.00) = -8.00 * (1 + 20.0/q)
1 = -8.00 + (-160/q)
Now, let's simplify further:
1 = -8.00 - 160/q
Combine like terms:
1 = (-8.00q - 160) / q
Now, let's cross-multiply:
q = (-8.00q - 160)
Move the terms with q to one side of the equation:
q + 8.00q = -160
Combine like terms:
9.00q = -160
Finally, solve for q by dividing both sides of the equation by 9.00:
q = -160 / 9.00
Calculating this, we get:
q ≈ -17.78 cm
Therefore, the position of the image is approximately q = -17.78 cm.