Board Thread:Fun and Games/@comment-33380803-20180418102023/@comment-30739178-20180511185245

The purpose of this investigation is to find the focal length of a concave spherical mirror, and the magnification at a certain distance.

First the focal length of the mirror was found when the object is far enough to be considered infinity (Part 1), then the focal length was found at different distances from object (Part 2), finally the magnification was found (Part 3). Materials: 
 * Light Source
 * Concave Mirror
 * Half-Screen
 * Ruler
 * Track to measure distances

Part I:

Procedure: Analysis: In the investigation we measured the distance between the mirror and the half-screen to be 9 cm, and when we solved for the focal length using the equation, f = 9 cm.
 * The mirror and the half-screen are held in separate hands
 * Focus a distant bright image on the half-screen using the mirror
 * Once the image is as focused as possible, the distance from the mirror to the half-screen is measured
 * Using the equation 1/f = 1/do + 1/di calculate the focal length (f)
 * do = distance from object
 * di = distance from image on the half-screen



Part 2:

Procedure: The results:
 * Place the light source at the front end of the measuring track with the light facing the rest of the track
 * Place the mirror 50 cm (do) away from the light source facing the light source
 * Place the half-screen between them
 * Move the half-screen until the image on it is at its clearest, measure the distance and record it
 * Repeat the previous steps with do 45, 40, 35, 30, and 25 cm
 * With do at 25 cm, measure the size of both the object and the image on the half-screen
 * Convert to 1/do and 1/di for all 6 trials

Next we plotted 1/do vs 1/di and found the best fir line where both the x and y intercepts will be equal to 1/f.

y-intercept = 0.104

x-intercept = 0.089

Using the intercepts we calculated f for both, found the percent difference between them and averaged them. We then foudn the percent difference between the focal length from part 1 and this average.

<p id="h.p_6cKSUxFRyqzv">y-intercept f = 9.615 cm

<p id="h.p_pEUAJvl0yvND">x-intercept f = 11.236 cm

<p id="h.p_z4n2XqBpyyY6">% difference = 14.43%

<p id="h.p_BmiBK7Jny1mT">Average = 10.42 cm

<p id="h.p_ldOQvKM6y7Yf">Result from Part 1 = 9 cm

<p id="h.p_Nk99aX8HzFDP">% difference - 13.63% <p id="h.p_Ocd5-0-yzM10">Part 3:

<p id="h.p_H63Jw7vezPEH">Procedure: <p id="h.p_Ag0rfoG8znUB">M = -(di/do) <p id="h.p_a1jd1nxaz-we">|M| = (image size)/(object size) <p id="h.p_3uay2edi0iS1">
 * Use the image and object sizes measured for do = 25 cm to calculate the magnification (M) using :
 * We then calculated the absolute value of M using:
 * Then we calculated the % differences between M and |M|

<p id="h.p_73bFN0CT0im-">Results:

<p id="h.p_646WV60M0jhn">M = -0.68

<p id="h.p_A-2GmPvw0qaF">|M| = -0.875

<p id="h.p_ETlLsTvG0tso">% Difference = 22.29%