d = \(\frac {1} { N }\), where N is the grating constant, and it is the number of lines per unit length. Also, n is the order of grating, which is a positive integer, representing the repetition of the spectrum.

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Typo Error> Speed of Light, C = 299,792,458 m/s in vacuum So U s/b C = 3 x 10^8 m/s Not that C = 3 x 108 m/s to imply C = 324 m/s A bullet is faster than 324m/s

These lenses eliminate parallax errors and provide consistent image magnification, making them ideal for precision measurement, machine vision, and microscopy. They offer improved depth of field and uniform image brightness. Telecentric lenses are constructed using complex optical designs, often including aspheric elements, to correct aberrations and maintain image quality across the field of view.

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A parallel bundle of the rays will fall on the grating. Rays and wavefront form an orthogonal set so the wavefront will be perpendicular to the rays and parallel to the grating. Here Huygens’ Principle is applicable.

There are mainly two types of telecentric lenses: object-space telecentric lenses and image-space telecentric lenses. Object-space telecentric lenses have parallel chief rays on the object side, while image-space telecentric lenses have parallel chief rays on the image side. Additionally, there are double telecentric lenses that combine both features.

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Consider two rays that emerge making the angle \(\theta\) with the straight through the line. Constructive interference will occur if the difference in their two path lengths is an integral multiple of their wavelength \(\lambda\) i.e.,

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If a peak falls on a valley consistently, then the waves cancel and no light exists at that point. Also, if peaks fall on peaks and valleys fall on valleys consistently, then the light is made brighter at that point. Diffraction is an alternative way to observe spectra other than a prism.

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Telecentric lenses are primarily used in applications requiring high precision and consistent imaging. These include machine vision systems for automated inspection and quality control, metrology for accurate dimensional measurements in manufacturing, and microscopy for detailed and distortion-free imaging in biological and material sciences. They are also crucial in semiconductor inspection, ensuring consistent magnification and eliminating parallax errors, making them ideal for industries where precise, repeatable measurements and uniform image brightness are essential.

A diffraction grating is made by making many parallel scratches on the surface of a flat piece of some transparent material. It is possible to put some large number of scratches per cm on the material. For example, the grating to be used has 6,000 lines per cm on it. The scratches are opaque but the areas between the scratches can transmit the light through. Thus, a diffraction grating becomes a multitude for the source with parallel slit, when light falls upon it. In this topic, a student will learn the diffraction grating formula with examples. Let us learn the concept!

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According to it every point on a wavefront acts as a new source, and each transparent slit becomes a new source so cylindrical wavefront spread out from each.

Furthermore, a complete spectrum could be observed for n = 1 and another complete spectrum for n = 2, etc., but at the larger angles.

A telecentric lens maintains constant magnification regardless of the object's distance or position along the optical axis. It achieves this by having parallel chief rays (rays that pass through the center of the aperture stop) which ensures the entrance pupil is effectively located at infinity. There are two main types: object-space telecentric, with parallel rays on the object side, and image-space telecentric, with parallel rays on the image side. Double telecentric lenses combine both features.

In this formula, \(\theta\) is the angle of emergence at which a wavelength will be bright. Also, d is the distance between slits. Obviously,

Q.1: A diffraction grating diffracts light at \(20 ^{\circ}\). What will be the wavelength of the light if the grating has 1000 lines per mm length?

Q.2: A diffraction grating has 36000 lines per cm and it separates a dark line at an angle of \(32 ^{\circ}\). Find the wavelength of the light.

Telecentric lenses offer several benefits, including consistent magnification regardless of object distance, eliminating parallax errors and ensuring precise measurements. They provide a uniform image brightness across the field of view and improve depth of field, maintaining sharpness over a greater range of distances. These lenses are ideal for high-precision applications such as machine vision, metrology, and microscopy, where accurate, distortion-free imaging is critical. Their design ensures reliable and repeatable measurements, enhancing overall imaging accuracy and quality.