Consider the Job Selection problem from lecture. You will modify the solution to this problem to work for a related problem. In lecture we had the rule that if you work one day you can’t work the next (or previous). In the modified problem you are allowed to work two days in a row but not three days in a row (so if you work 2 days in a row you can’t work the day before these 2 days or the day after). 1. Express the modified problem formally with input and output conditions. 2. State a self-reduction for your problem. Use the self-reduction from lecture as inspiration. 3. State a dynamic programming algorithm based off of your self reduction that computes the maximum earnings. 4. Design a function that recovers the days that must be worked to achieve the maximum earnings. 5. Compute the maximum earnings and the days to work for this input P=[5, 9, 12, 7, 5, 13, 7, 5, 4, 9, 8, 7, 5, 8, 4, 3, 5, 10, 4, 6, 8, 12, 5, 6, 3, 7, 16, 2, 2, 16] 6. What are the worst case time and space requirements of your complete solution?

Infrared sensor is most used sensor in wireless technology where remote controlling functions and detection of surrounding objects/ obstacles are involved. this post will discuss about what is infrared sensor, its working principle, how it works, types, applications, advantages and disadvantages. what is infrared sensor

ir sensor is a simple electronic device which emits and detects ir radiation in order to find out certain objects/obstacles in its range. some of its features are heat and motion sensing.

ir sensors use infrared radiation of wavelength between 0.75 to 1000µm which falls between visible and microwave regions of electromagnetic spectrum. ir region is not visible to human eyes. infrared spectrum is categorized into three regions based on its wavelength i.e. near infrared, mid infrared, far infrared.

wavelength regions of infrared spectrum

near ir – 0.75µm to 3 µm
mid ir – 3 µm to 6 µm
far ir – > 6 µm
1 introduction to infrared sensor

fig. 1 – introduction to infrared sensor

working principle of infrared sensor

infrared sensors works on three fundamental physics laws:

planck’s radiation law: any object whose temperature is not equal to absolute zero (0 kelvin) emits radiation.
stephan boltzmann law: the total energy emitted at all wavelengths by a black body is related to the absolute temperature.
wein’s displacement law: objects of different temperature emit spectra that peak at different wavelengths that is inversely proportional to temperature.
key elements of infrared detection system

the key elements of infrared detection system are:

ir transmitter

ir transmitter acts as source for ir radiation. according to plank’s radiation law, every object is a source of ir radiation at temp t above 0 kelvin. in most cases black body radiators, tungsten lamps, silicon carbide, infrared lasers, leds of infrared wavelength are used as sources.

transmission medium

as the name suggests, transmission medium provides passage for the radiation to reach from ir transmitter to ir receiver. vacuum, atmosphere and optical fibers are used as medium.

ir receiver

generally ir receivers are photo diode and photo transistors. they are capable of detecting infrared radiation. hence ir receiver is also called as ir detector. variety of receivers are available based on wavelength, voltage and package.

ir transmitter and receivers are selected with matching parameters. some of deciding specifications of receivers are photosensitivity or responsivity, noise equivalent power and detectivity.