Interference of light. Determination of lens curvature radius and light wavelength using Newton's rings

The purpose of the work: to study light interference phenomena; to determine lens curvature radius and light wavelength by measuring Newton's rings diameters

Devices and accessories: 1. plane-parallel plate, plano-convex lens; 2. light source; 3. microscope

Task 1. Determination of Newton’s rings diameters

1. Measure points of microscope scale. Enter the results into table 1.

2. Calculate the Newton’s rings diameters as microscope scale readings difference. Enter the results into table 1.

Table 1

Exp. No	Ring number, k	Left-hand reading, mm	Right-hand reading, mm	Ring diameter, D, mm	Ring diameter mean value Dave, mm	mm2	, m	, %
1	1
	2
	3
	4
	5
	6
2	1
	2
	3
	4
	5
	6
3	1
	2
	3
	4
	5
	6

1.3. Determine error of the Newton’s rings diameters measurement. Carry out calculations, for example, for the fourth ring.

— Calculate mean value of diameter of the fourth ring:

— Calculate random deviation of every measured diameter from diameter mean value according to the formula:

— Determine root-mean-square deviations according to the formula:

— Determine the absolute error of diameter measurement according to the formula:

where the Student’s coefficient is t_St = 4,3 (m = 3 and  = 0,95).

— Determine the fractional error of diameter measurement according to the formula:

• Write down the result in the following form:

, m.

Task 2. Calculation of lens curvature radius

2.1. Calculate lens curvature radius according to the formula:

, m.

Enter the results into table 2.

Table 2

Ring number combination

k

i

k

i

k

i

k

i

k

i

k

i

k

i

k

i

k

i

k

i

k

i

k

i

k

i

k

i

k

i

6

5

6

4

6

3

6

2

6

1

5

4

5

3

5

2

5

1

4

3

4

2

4

1

3

2

3

1

2

1

Radius of lens curvature, Rm, m

R1

R2

R3

R4

R5

R6

R7

R8

R9

R10

R11

R12

R13

R14

R15

Task 3. Determination of the absolute and the fractional errors of lens curvature radius measurement

3.1. Calculate mean value of lens curvature radius according to the formula:

.

Enter the results into table 3.

3.2. Calculate random deviation of every radius from its mean value according to the formula:

Enter the results into table 3.

3.3. Determine root-mean-square deviations according to the formula:

3.4. Determine the absolute error of diameter measurement according to the formula:

where the Student’s coefficient is t_St = 1,83 (m = 15 and  = 0,95).

3.5. Determine the fractional error of lens curvature radius measurement according to the formula:

.

3.6. Write down the result in a form:

, m

Enter the results into table 3.

Table 3

Mean value of lens curvature radius Rave, m	Absolute error, R, m	Fractional error, , %	Lens curvature radius determined by graphical method, R, m	Difference between lens curvature radius determination, %

Task 4. Determination of lens curvature radius by graphical method

4.1. Plot graph, putting on axis of ordinates and number of rings on abscissa axis:

4.2. Determine lens curvature radius according to the formula:

4.3. Compare lens curvature radius obtained by analytical and graphical methods. Determine the difference between lens curvature radius determinations according to the formula:

.

Enter the results into table 3.

Task 5. Determination of air clearance thickness

5.1. Determine air clearance thickness between the plano-convex lens and the plane glass plate according to the formula:

Enter the results into table 4.

Task 6. Determination of half-wavelength amount

6.1. Determine the amount of half-wavelength according to formulae:

Enter the results into table 4.