Q.How does photocurrent vary with the intensity of the incident light?

The photoelectric effect obeys three key experimental laws relating intensity, frequency, and the kinetic energy/timing of emitted photoelectrons.

1. Law of intensity (saturation photocurrent). For light of a fixed frequency $\nu$ (greater than the threshold frequency) incident on a given photosensitive metal, the photoelectric current (i.e., the number of photoelectrons emitted per second) is directly proportional to the intensity of the incident light, provided the frequency and the retarding/accelerating potential are held fixed.

2. Law of threshold frequency. For every photosensitive metal there is a minimum frequency of incident light, called the threshold frequency $\nu_0$, below which no photoelectric emission takes place at all, however great the intensity of the light or however long it is shone on the surface. Emission begins the instant $\nu \ge\nu_0$.

3. Law of maximum kinetic energy. The maximum kinetic energy of the emitted photoelectrons is found to depend only on the frequency of the incident light (increasing linearly with $\nu$ above $\nu_0$, as $KE_{max}=h\nu-\phi$) and is completely independent of the intensity of the light. Increasing intensity increases the number of photoelectrons, not their maximum energy.

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The four experimental laws of the photoelectric effect concern how photocurrent, threshold frequency, maximum kinetic energy, and emission time relate to the light's intensity and frequency.

1. Law of intensity (photoelectric current): for light of a given frequency (above the threshold), the number of photoelectrons emitted per second (i.e. the photoelectric/saturation current) is directly proportional to the intensity of the incident light.
2. Threshold frequency: for a given metal surface, there exists a minimum (threshold) frequency $\nu_0$ of incident light, below which no photoelectrons are emitted at all, no matter how intense the light is.
3. Maximum kinetic energy law: above the threshold frequency, the maximum kinetic energy of the emitted photoelectrons is independent of the intensity of the incident light, but increases linearly with the frequency of the incident light (as given by Einstein's photoelectric equation, $KE_{max}=h\nu-\phi_0$). …