Calculating Distance from Mirror for Virtual Image Height of 1.145 cm

AI Thread Summary
To calculate the distance from a concave mirror for a virtual image height of 1.145 cm, the object height is given as 0.375 cm and its initial distance is 10.5 cm. The radius of curvature of the mirror is determined to be 15.8 cm, leading to a focal length of 7.9 cm. The relationship between object distance (S), image distance (Si), and their respective heights is established using the equations 1/S + 1/Si = 1/f and Hi/H = -Si/S. The challenge lies in adjusting the equations to account for the virtual image, which requires careful consideration of the signs in the formulas. Ultimately, solving for S in terms of Si will yield the necessary object distance for the desired virtual image height.
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Homework Statement


An object whose height is 0.375 cm is at a distance of 10.5 cm from a spherical concave mirror. Its image is real and has a height of 1.145 cm. Calculate the radius of curvature of the mirror.

Correct, computer gets: 1.58e+01 cm

ACTUAL QUESTION
How far from the mirror is it necessary to place the above object in order to have a virtual image with a height of 1.145 cm?


Homework Equations


1/S + 1/Si = 2/R = 1/f
Hi/H = -Si/S


The Attempt at a Solution


I am not sure how to relate the equations...Also, I am unsure as to how the image being virtual in the actual question changes things. I know f=R/2 = 7.9cm

Homework Statement

 
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Using Hi/H = -Si/S find S in terms of Si. Put it in the equation 1/S + 1/Si = 2/R = 1/f with proper sign of S, Si and f. Solve for S.
 

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