WARNING! Never (not even through a solution of potassium permanganate) should you shine a laser pointer into your own eyes or those of other participants!

Attention! The problem does not require error estimation in tasks where this is not explicitly stated.

Equipment:

1. Multimeter
2. Banana-to-banana wire
3. Cuvette with potassium permanganate solution. Do not open!
4. Infrared LED
5. Photodiode
6. AA battery holder (2 batteries) for connecting to the LED
7. 9V battery holder for connecting to the photodiode
8. Laser pointer
9. Laser pointer stand
10. Clip for holding the laser pointer button
11. Diffraction grating on a holder
12. Aperture
13. Goniometer

To measure the intensity of light incident on the photodiode, connect the following components in series: the photodiode, a multimeter operating in voltmeter mode, and a 9V battery. The red terminal of the 9V battery should be connected to the red terminal of the photodiode. The voltmeter can be used to measure the current flowing through the photodiode. This current is referred to as the photocurrent. Throughout all parts of the problem, the voltmeter's internal resistance is considered known and equal to $R_V =1~\text{M} \Omega$

Note. If the voltmeter reading under this connection reaches the battery voltage ($\sim 10~V$), further increase in the light intensity incident on the photodiode will not change the voltmeter's readings. Therefore, effective measurement of the light intensity incident on the photodiode is only possible when the voltmeter shows voltages $< 9~V$.

To power the LED, connect the LED and two AA batteries. The red terminal of the battery holder should be connected to the red terminal of the LED.

Warning! Do not connect the LED to the 9V battery! This will damage it. The LED will not be replaced.

The current-voltage characteristic of the photodiode connected according to the instructions, under two different illumination levels, is shown in Fig. 1. Starting from approximately $\sim 2~V$, the curve reaches current saturation. This saturated current is measured in the experiment.

Part 1. Photodetector Linearity

Mount the LED and photodiode on the goniometer as shown in Fig. 2. The LED is placed on the long arm of the goniometer, while the photodiode is on the short arm. Align the LED body and the photosensitive surface of the photodiode at the same height. The distance between the LED and photodiode can be adjusted by moving the LED along the long arm of the goniometer.

1.1 Measure the dependence of the photodiode's photocurrent on the distance between the photodiode's surface and the nearest point of the LED body.

1.2 Disconnect the LED power circuit. Measure the background photodiode current with an accuracy of at least $5 \%$. Estimate the measurement error. Modify the measurement circuit if necessary.

1.3 Check if the photodiode current is proportional to the intensity of light incident on it for voltmeter voltages $< 9~V$. To do this, plot the measured dependence in linearized form and draw the appropriate conclusion.

Part 2. LED Radiation Pattern

Mount the LED on the goniometer so that its body is centered (see Fig. 3). Position the photodiode on the goniometer's short arm. Align the height of the LED body with the photodiode's measurement plane, as done previously.

2.1 Apply voltage to the LED from two AA batteries. By changing the relative position of the photodiode and LED, measure the dependence of the photodiode current on the angle $\varphi$ between the LED axis and the line connecting the LED tip to the center point of the photodiode's measurement surface.

2.2 Plot the measured dependence. Determine the angle at which the photocurrent decreases by a factor of 5.

Part 3. LED Emission Spectrum

Attach the aperture to the diffraction grating. Mount the diffraction grating with the aperture at the center of the goniometer, aligning its plane perpendicular to the direction of the goniometer's long arm (see Fig. 4). Install the LED on the long arm and the photodiode on the short arm of the goniometer. Determine optimal distances between components experimentally. Align the height of the LED body with the photodiode's measurement surface.

The setup allows measuring the LED's emission spectrum (see Fig. 5). The emission spectrum has a peak at wavelength $\lambda_{led}$.

3.1 Rotate the goniometer's short arm relative to the long arm to determine the angle $\varphi_1$ corresponding to the first diffraction maximum at wavelength $\lambda_{led}$. During measurements, ensure that the LED radiation does not reach the photodiode directly, bypassing the diffraction grating.

3.2 Calculate the wavelength of the LED's emission spectrum peak $\lambda_{led}$.

Part 4. Green Laser Emission Spectrum

Replace the LED with the laser pointer (see Fig. 6). Hold the green laser's button with the clip. Adjust the photodiode height and diffraction grating position so that all visually observable diffraction maxima of the green laser reach the photodiode when rotating the goniometer's short arm relative to the long arm.

4.1 Measure the dependence of the photodiode current on the angle between the laser axis and the line connecting the diffraction grating slit center to the photodiode's measurement surface center by varying their relative positions. For each photodiode position, block the laser beam at its output window and measure the background current. Take measurements from 0 to 40 degrees in 1-degree increments.

4.2 Calculate the photocurrent difference with and without laser radiation at the photodiode's zero position $\left(I_{p h}-I_{p h 0}\right)(\varphi=0)$. Calculate the photocurrent difference with and without laser radiation across all measured angles
$\left(I_{p h}-I_{p h 0}\right)(\varphi)$.

Plot the natural logarithm of the ratio of measured quantities
$\ln\dfrac{\left(I_{p h}-I_{p h 0}\right)(\varphi)}{\left(I_{p h}-I_{p h 0}\right)(\varphi=0)}$ versus angle $\varphi$. We will call this dependence as the diffraction pattern spectrum.

4.3 Specify the angles of the diffraction pattern spectrum maxima (excluding zero). Which of these angles correspond to the laser emission wavelength at $\lambda_1=532 \ nm$?

4.4 Place the cuvette with potassium permanganate solution in the path of the laser beam. Indicate whether the green laser spot is visible after passing through the potassium permanganate.

4.5 Measure the diffraction pattern spectrum again. Take measurements in the range from 0 to 40 degrees.

4.6 Plot the measured spectrum.

4.7 Specify the wavelengths of peaks of the laser emission spectrum. Explain the obtained result.