The relationship between output signal and input light intensity of a light intensity transducer is:

Explanation:

Relationship between Output Signal and Input Light Intensity of a Light Intensity Transducer

Definition: A light intensity transducer is a device that converts light intensity into an electrical signal, which can be used for measurement and control purposes. The relationship between the output signal (V₀) and input light intensity (Q) is determined by the characteristics of the transducer and the nature of the underlying physical principle.

Correct Option Analysis:

The correct option is:

Option 3: V₀ = K × e^-αQ

This equation represents an exponential decay relationship between the output signal (V₀) and the input light intensity (Q). In this relationship:

• K: A proportionality constant that depends on the specific characteristics of the transducer.
• α: A constant that defines the sensitivity of the transducer to changes in light intensity.
• Q: The input light intensity.

As light intensity (Q) increases, the exponential term e^-αQ decreases, leading to a decrease in the output signal (V₀). This behavior is characteristic of certain types of transducers, where the output signal reduces with increasing light intensity due to saturation effects or specific material properties.

Explanation of the Correct Option:

The exponential decay relationship described by V₀ = K × e^-αQ is commonly observed in photodetectors or light sensors where the response is non-linear. For instance:

• In semiconductors, the absorption of light can cause changes in carrier concentration, leading to a non-linear output signal.
• The exponential decay may also result from the characteristics of the photodetector's material, where higher light intensities saturate the device, reducing its sensitivity.

In practical applications, this relationship is useful for designing systems that require precise control of light intensity, such as optical communication systems, light measurement devices, and automatic brightness control in displays.

Important Note: The constants K and α need to be experimentally determined for a specific transducer and application.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: V₀ = K × e^αQ

This option suggests an exponential growth relationship, where the output signal increases exponentially with increasing light intensity. However, this is not consistent with the typical behavior of light intensity transducers, as most transducers exhibit saturation effects or exponential decay at higher light intensities. Therefore, this option is incorrect.

Option 2: V₀ = K × e^α/Q

This option implies an inverse relationship between the output signal and the input light intensity (Q). While inverse relationships can be observed in certain systems, it is not applicable to the behavior of light intensity transducers described in this context. Hence, this option is incorrect.

Option 4: V₀ = K × e^-α/Q

Similar to option 2, this equation represents an inverse relationship, with an additional exponential decay factor. However, this does not align with the observed behavior of light intensity transducers where the output signal decays exponentially with increasing light intensity. Thus, this option is also incorrect.

Conclusion:

Among the given options, the correct relationship between the output signal (V₀) and the input light intensity (Q) for a light intensity transducer is best described by the equation V₀ = K × e^-αQ. This relationship accurately represents the exponential decay behavior observed in many light intensity transducers, making it suitable for practical applications in measurement and control systems.