Experiment 8

Reflection of Light (Spherical Mirrors)

Objective:

 

   The objective is to verify the mirrors formula by forming the image of an object in a converging and diverging mirrors.

 

Equipment:

 

   A computer with internet connection, a calculator, a ruler, a few sheets of paper, and a pencil

 

Theory:

 

The spherical mirrors formula is

where  do is the object distance from the mirror,  d, the image distance from the mirror, and  f , the focal length of the mirror.    f = R/2 and R is the radius of the mirror.  Assigning a (-) sign to di indicates advance knowledge of a virtual image and obtaining a (-) value for the image through solving this equation for di indicates a virtual image as well.

 

For a diverging mirror,  f , the focal length should be given a  (-) sign when using the above equation because for a diverging mirror, the focal point is virtual.  In general, anything virtual is negative, and anything real is positive.

 

Magnification:  Magnification is the ratio of the image size to the object size The absolute value of magnification is given by the following formula:

 

The absolute value of magnification is also the ratio of image distance to the object distance.

 

Ray Diagrams for a Converging Mirror:

 

There are six different cases for image of an object in a converging mirror.

 

Case I : Object at infinity  (do >> 2f )

 

Rays coming from very far away are practically parallel.  If such rays are also parallel to the main axis of the mirror, the image forms at F, the focal point of the mirror, as shown:

 

Image:

1) Real           2) Inverted

3) A'B'<<AB   

4)  di = f

 

 

Case II:  Object beyond 2f  (do > 2f )

 

 

Image:

1)Real                    2) Inverted

3) A'B' < AB         4) f < di < 2f

 

 

Infinite rays emerge from any point of object AB, including Point A of it.  Two rays are selected.  Important Ray 1 that travels parallel to the main axis passes through F, after reflection.   Important Ray 2 that goes through F leaves the mirror parallel to the mail axis, after reflection.  The intersection of the two reflected rays form A', the image of A.   

 

Case III: Object at 2f  (do = 2f )

Image:

1) Real                 2) Inverted

3) A'B' = AB        

4) di = 2f

 

Case IV: Object between f and 2f  ( f < do < 2f )

Image:

1) Real                    2) Inverted

3) A'B' > AB           4) di > 2f

 

 

Case V: Object at F  (do  = f )

Image:

1) Real                      2) Inverted

3) A'B' >> AB          4)  di → ∞

 

 

Case V': Object slightly beyond F  (do ~ f )

 

 

Case VI: Object within f  (do < f )

 

Image:

1) Virtual                   2) Upright

3) A'B' >AB    

4)  di behind the mirror. Image forms behind the mirror.

 

 

 

 

For Practice: 

 

Use two out of three important rays emerging from A to form its image A' and complete each of the following ray diagrams:

Note that A' is found by the intersection of rays reflected from the mirror.  Also state the image conditions.

 

 

 

 

Image in Diverging Mirrors

 

The image formed by a diverging (convex) mirror is always virtual, upright, smaller than the object, and behind the mirror.

 

 A ray diagram is shown below:

 

Image:

1) Virtual             2) Upright

3) A'B' <AB    

4)  di behind the mirror

 

 

Practice on Image in a Diverging Mirror

 

Complete the ray diagram shown below:

Procedure:

 

Click on the following link:  http://surendranath.tripod.com/Applets.html .    Click on the "Applet Menu", then on "Optics", and then click on "Spherical Mirrors and Lenses."  The applet asks you to click on it to start.  Click on the applet.  The screen for the experiment (or the Optical Bench) appears.  On the top left dropdown menu, click on "Concave Mirror" if it is not already on the bench.  Two yellow spots on the main axis of the mirror show its center and focal point   Each square is a 20 units by 20 units.  If you hold the mouse on the mirror itself where it crosses the main axis, you can move it left or right and place it where you like. The mirror allows you select a focal length for it.  If you place the mouse on F and move it left or right, the focal length changes and so does the radius (or the location of C accordingly because R = 2f).  As you move F, theconcavity of the mirror changes.  The more concave a mirror gets, the shorter its focal length becomes.  We are going to think of (mm) as the unit of length in this experiment; therefore, if the applet says f = 100.0, it means f = 100.0mm.   On this basis, each square on the applet is 20mmX20mm.

Important: In the Mirror's Formula, all distances are measured from the mirror itself for the formula to predict correctly.

 

Experiment:

 

Part 1, Concave Mirrors (Converging Mirrors):

 

1) Make sure that the converging mirror is exactly in the middle (20 squares on the left and 20 squares on the right of it).  Set F (the Focal Point) at 120mm, or let f = 120mm.  Read the top of the applet to make sure it reads f = 120mm. 

2) Place the mouse at the tip of the object (the red arrow) and make its height equal to 4 squares or 80.0mm.  Also move it to the far left at do = 400.0mm.  Check the values of y ( the object height), and do on the top to assure their correctness.

3) Measure (estimate) the position of di on the applet and record your estimate in Table 1.   Estimate the height of the image, y',  on the applet and record your estimate in Table 1.  These will be your measured values.   In estimation, each square has a length of 20.0mm.

4) Use the given values of do and f to calculate the expected di   This will be the accepted value for di .   Use this di and do to find the magnification, M.   Then use the magnification, M to calculate y' (the image height).  This will be the accepted value for y'.  Record all values in Table 1.

5) Keeping the same object height of y = 80.0mm, and f = 120mm, and repeat the above steps for the following do values:  240.0mm, 170.0mm, 130.0mm, 121.0mm, 119.0mm, and 70.0mm. 

Note:  In cases that the image goes out of screen, just calculate the accepted value for di and y', and leave the space for the measured values blank and do not calculate their respective % errors.

 

Part 2, Convex Mirrors (diverging Mirrors):

1) Change the mirror to a convex one by clicking on the "Convex Mirror" in the top left dropdown window.  A convex Mirror will appear.  With the mouse, place the mirror exactly at the16th square from the right side of the screen.  The screen is 60 squares wide.  Now, there must be exactly 16 squares to the right of the mirror and 44 to its left.

2) Move the virtual focal point F to 8 squares from the mirror such that f = 160.0mm.  This places the virtual center of the mirror at the rightmost edge of the matrix (R = 320mm).  Make sure the applet reads the same.  Of course, you know that the focal point and focal length of a convex mirror are both virtual.  The f to be used in calculations is actually f = -160.0mm.

3) Keep the same height of y = 80.0mm and move the object 3 squares away from the mirror at do = 60.0mm.  Double-check your readings for f, do , and y.

4) Again, measure (estimate) di and y'.  These will be your measured (estimated) values.

5) Using do , f, and y,  calculate the accepted values for di , M, and y'.

6) Finally calculate the necessary % errors.

7) Keep the same object height of y = 80.0mm, and f = -160.0mm, repeat the above steps for the following do values:  120.0mm, 230.0mm, 320.0mm, 500.0mm, and 720.0mm.  Do all related calculations for each case and record the values in Table 1.

Data:

        Given and Measured:

Table 1

 

Case

Object's

 Distance

do

(mm)  

Focal

 Length

f

(mm) 

 Measured

(Estimate)

Image Dist.

 di  (mm)

 Accepted

 Calculated

Image Dist.

di  (mm)

Absolute Value of Magnifi -cation

M

Object's

Height

y

(mm)

Measured

Image Size

y'

(mm)

Accepted

Image Size

y'

(mm)

%

Error

on

di

 

%

Error

on

y'

 

Concave Mirror:

 

 

 

80.0

 

 

 

 

1

400.0

+120.

 

 

 

80.0

 

 

 

 

2

240.0

+120.

 

 

 

80.0

 

 

 

 

3

170.0

+120.

 

 

 

80.0

 

 

 

 

4

130.0

+120.

 

 

 

80.0

 

 

 

 

5

121.0

+120.

 

 

 

80.0

 

 

 

 

6

119.0

+120.

 

 

 

80.0

 

 

 

 

7

70.0

+120.

 

 

 

80.0

 

 

 

 

Convex Mirror:

Virtual Image Position ( di ) is Negative                    

8

120.0

-160.0

-           

-           

 

80.0

 

 

 

 

9

230.0

-160.0

-           

-           

 

80.0

 

 

 

 

10

320.0

-160.0

-           

-           

 

80.0

 

 

 

 

11

500.0

-160.0

-           

-           

 

80.0

 

 

 

 

12

720.0

-160.0

-           

-           

 

80.0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Calculations:

 

Use the Mirror's Formula and the Magnification Formula to perform calculations.

 

Comparison of the Results:

 

Calculate a % error on di and y' for each case using the usual % error formula.

                       

Conclusion:  To be explained by students

 

Discussion:   To be explained by students