Aberration

...

Minimum, cm

Maximum, cm

Most probable, cm

Average, cm

Focal length, cm

w/o iris:

79,5

81,9

80,0

80,5

7,53

w/ iris and totally open:

79,3

84,1

80,5

81,3

7,58

w/ iris and wider opening:

78,6

85,8

82,3

82,2

7,63

w/ iris and narrow opening:

80,5

89,1

84,1

84,6

7,76

Table 1. Positions of the image produced by plano-convex lens (f = 7.5cm)

As you can see, when we inserted the iris, the position of the clear image has been considerably increased, consequently, the focal length also increased. This means that the rays that passes through outer regions of the lens, which focuses nearer to the lens has been filtered by the iris, so focusing the rays farther away from its actual position. The actual focal length of the lens is about 7.5cm, but this should be compared with the case of the setup without iris. The reason why we use the data of without iris is that, when manufacturer designed the lens, he may assumed the lens to perform well alone in the setup at f = 7.5cm. If one wishes to measure the focal length by using the position of “Most probable” image, then it reveals exactly 7.50 cm.

Moreover, another thing that you may easily notice from the table 1 is that as the iris is inserted into the rail and as being decreased its size, the interval of clearer image has been increased. For example, if in case of without iris it was ~2.4 cm, after the iris was inserted and decreased in size, I became ~8.6 cm.

Next we repeated the same experiment, but in this case using the biconvex lens (f =10cm) at x = 60cm in place of the previous lens and the distance between object and lens is about 14cm. Finally, obtained the following data:

Minimum, cm

Maximum, cm

Average, cm

Focal length, cm

w/o iris:

94,1

96,1

95,1

10,0

w/ iris and open:

94,5

97,5

96,0

10,1

w/ iris and wider opening:

95,2

98,9

97,1

10,2

w/ iris and narrow opening:

95,3

105,0

100,2

10,4

Table 2. Positions of the image produced by bi-convex lens (f = 10 cm)

In this case we can notice that the focal length did vary more than the previous case, this is because as the focal length increases, the deviation in the image distance also increases. However, another main factor if we could place our object more father from the lens, then image distance would decrease, leading to the decrease in deviations. Actually, the most accurate situation can occur, when the object distance and the image distance are close to each other, avoiding the ill-conditioned system. Moreover, the experimental value of the focal length and the value given by the manufacturer are the same.

In addition, here it is also clearly noticeable that the as the iris being inserted, the interval of the clear image position was also increased dramatically.

Curvature of Field

The experimental setup is the same as in spherical aberrations, except, in this case an object was replaced by transmission letter and plano-convex (f = 7.5 cm) was used. While moving the screen away, we could observe that the rectangular edges of the transmission letter in fig.10 (a) has been tortured as in fig 10. (b). Moreover, there is a distortion also can be noticed at the margins of the letter.

Fig. 10 (a) True image Fig. 10. (b) Suffered image from curvature of field

Astigmatism

In this experimental setup, we used an iris as an object, and other setup was the same as in the previous part of the experiment. The image of the circular hole of the iris is depicted in fig 11(a). After we have changed the aperture height of the iris, we obtained an elliptic circle as in fig 11(b). Moreover, moving the screen towards the lens, it has decreased, converging to the very small ellipse with very narrow minor axis than the major axis (our camera could not catch that). It finally led to a very small dot like circle, and converged back to an ellipse as in fig. 11(c). This is because of the astigmatism.

Fig. 11 (a) true image Fig. 11 (b) Secondary Image Fig. 11 (a) Primary image

Coma

This part needs only He-Ne laser, beam expander which is used as an object, plano-convex (f = 7.5 cm) and screen, and they are set up in the optical rail respectively. In the fig.12 (a), there is an image of beam expander, and in 12(b), there is a comet like image of that object when the plano-convex