physics - image distance question. please help :)

Question

Calculate the image distance for a object that is 14.2 cm away from a concave mirror that has a focal length of 5.8 cm.

in terms of centimeters. 
to a precision of tenths of a centimeter. 
to an accuracy of 0.2 cm. 

 

 

thank you! :)

Answer 1

First, you'll need the concave mirror equation:

 

1/f = 1/d_object + 1/d_image

 

so to solve for d_image (we'll just abbreviate it to d_i from now on):

 

1/d_i = 1/f - 1/d_o

 

1/d_i = (d_o-f) / (f*d_o)

 

Thus taking the reciprocal of both sides:

 

d_i = (f*d_o) / (d_o-f)

 

Ok, so now plug in the numbers:

 

d_i = (5.8*14.2) / (14.2 - 5.8)

= 82.36 / 8.4

= 9.805 centimeters

 

Rounding to the nearest tenth of a centimeter, the answer becomes 9.8 cm.

 

As far as accuracy is concerned, 0.2 cm indicates that your answer falls in line with +/- 0.1 cm

 

So your answer would be 9.8 +/- 0.1 cm