9.30 A Cassegrain telescope uses two mirrors as shown in Fig. 9.30. Such a telescope is built with the mirrors 20 mm apart. If the radius of curvature of the large mirror is 220 mm and the small mirror is 140 mm, where will the final image of an object at infinity be?
9.30 Distance between the objective mirror and the secondary mirror, d = 20 mm
Radius of curvature of objective mirror, = 220 mm
Hence focal length of the objective mirror, = = 110 mm
Radius of curvature of secondary mirror, = 140 mm
Hence focal length of the objective mirror, = = 70 mm
The image of an object placed at infinity, formed by the objective mirror, will act as a virtual object for the secondary mirror. Hence, the virtual object distance for the secondary mirror,
u = = 110 – 20 = 90 mm
Applying the mirror formula for the secondary mirror, we can cal
...more
9.30 Distance between the objective mirror and the secondary mirror, d = 20 mm
Radius of curvature of objective mirror, = 220 mm
Hence focal length of the objective mirror, = = 110 mm
Radius of curvature of secondary mirror, = 140 mm
Hence focal length of the objective mirror, = = 70 mm
The image of an object placed at infinity, formed by the objective mirror, will act as a virtual object for the secondary mirror. Hence, the virtual object distance for the secondary mirror,
u = = 110 – 20 = 90 mm
Applying the mirror formula for the secondary mirror, we can calculate the image distance ( ) as:
+ = or = = -
= 315 mm
Hence, the final image will be formed 315 mm away from the secondary mirror.
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<p><strong>9.30 </strong>Distance between the objective mirror and the secondary mirror, d = 20 mm</p><p>Radius of curvature of objective mirror, <span title="Click to copy mathml"><math><msub><mrow><mrow><mi>R</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></math></span> = 220 mm</p><p>Hence focal length of the objective mirror, <span title="Click to copy mathml"><math><msub><mrow><mrow><mi>f</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></math></span> = <span title="Click to copy mathml"><math><mfrac><mrow><mrow><msub><mrow><mrow><mi>R</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></mfrac></math></span> = 110 mm</p><p>Radius of curvature of secondary mirror, <span title="Click to copy mathml"><math><msub><mrow><mrow><mi>R</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></math></span> = 140 mm</p><p>Hence focal length of the objective mirror, <span title="Click to copy mathml"><math><msub><mrow><mrow><mi>f</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></math></span> = <span title="Click to copy mathml"><math><mfrac><mrow><mrow><msub><mrow><mrow><mi>R</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></mfrac></math></span> = 70 mm</p><p>The image of an object placed at infinity, formed by the objective mirror, will act as a virtual object for the secondary mirror. Hence, the virtual object distance for the secondary mirror, </p><p>u = <span title="Click to copy mathml"><math><msub><mrow><mrow><mi>f</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub><mo>-</mo><mi></mi><mi>d</mi></math></span> = 110 – 20 = 90 mm</p><p>Applying the mirror formula for the secondary mirror, we can calculate the image distance ( <span title="Click to copy mathml"><math><mi>v</mi></math></span> ) as:</p><p><span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mi>v</mi></mrow></mrow></mfrac></math></span> + <span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mi>u</mi></mrow></mrow></mfrac></math></span> = <span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><msub><mrow><mrow><mi>f</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></mrow></mrow></mfrac></math></span> or <span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mi>v</mi></mrow></mrow></mfrac></math></span> = <span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><msub><mrow><mrow><mi>f</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></mrow></mrow></mfrac><mo>-</mo><mi></mi><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mi>u</mi></mrow></mrow></mfrac></math></span> = <span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mn>70</mn></mrow></mrow></mfrac></math></span> - <span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mn>90</mn></mrow></mrow></mfrac></math></span></p><p><span title="Click to copy mathml"><math><mi>v</mi></math></span> = 315 mm</p><p>Hence, the final image will be formed 315 mm away from the secondary mirror.</p>
A total refractive prism is also known as a total internal reflection prism. It is an optical prism that is designed for reflecting 100% of the incident light. This happens since this prism uses the principle of total internal reflection. These prisms are oriented and shaped in a specific way so that the light that enters at a specific angle is completely reflected inside the prism. A right-angle prism, porro prism, dove prism and roof prism are some of the examples of total reflective prism.
Total deviation in a prism is the total angle by which the light ray gets bent as it passes through the prism. It is an angle between incident ray and emergent ray of the prism. When a light enters the prism, it will bend towards the normal. After that, it will travel through the prism and bend away from the normal as it exits. Total deviation is the sum of these two from which the apex angle is subtracted.
The formula for total deviation for a prism is as follows:
There are different types of glasses that are used in optical instruments, including the following:
Crown glass (K): This glass is used in eyeglasses, microscopes and cameras. It is used in prisms and windows in optical systems. Crown glass has a low refractive index, low dispersion and excellent transparency in visible spectrum.
Flint Glass (F): This glass, when combined with crown glass, can correct chromatic aberration in lenses. They are also used in prisms for spectroscopy.
Extra-low dispersion glass: These glasses are used in premium optics that are also used for making high-quality camera lenses, telescopes and binoculars.
Optical instruments can have some of the following defects that may impact their performance, which have arisen due to design limitations, manufacturing and physical properties of light:
Chromatic Aberration: This defect occurs because of the different wavelengths of light that refract at slightly different angles when they pass through the lens. It causes them to focus on different points.
Spherical Aberration: This happens because light rays pass through the edges of spherical lens or reflect off spherical mirror focus at different point than rays that pass through the center.
Astigmatism: This type of defect occurs due to the uneven cu
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Optical instruments can have some of the following defects that may impact their performance, which have arisen due to design limitations, manufacturing and physical properties of light:
Chromatic Aberration: This defect occurs because of the different wavelengths of light that refract at slightly different angles when they pass through the lens. It causes them to focus on different points.
Spherical Aberration: This happens because light rays pass through the edges of spherical lens or reflect off spherical mirror focus at different point than rays that pass through the center.
Astigmatism: This type of defect occurs due to the uneven curvature of lenses or mirrors, which causes light to focus differently in horizontal and vertical planes.
Field Curvature: One of the defects in optical instruments is field curvature, which occurs due to flat image sensors and film that cannot perfectly match the curved focal plane of a lens.
Yes, optical instruments are used in modern medicine for many purposes including surgery, monitoring, research and diagnosis. Let us take a look at each one by one:
Many optical instruments are used for visualizing internal structures for diagnosis of a disease and its monitoring. These include Ophthalmoscope, Endoscope, Colposcope and Dermatoscope.
Optical instruments are also used for precision and minimally invasive surgeries, including Laparoscope, Arthroscope and Surgical Microscopes.
Lasers are used for cutting, therapy and coagulation since they have precision and minimal invasiveness. CO? Laser, Excimer Laser and Fiber Optic
...more
Yes, optical instruments are used in modern medicine for many purposes including surgery, monitoring, research and diagnosis. Let us take a look at each one by one:
Many optical instruments are used for visualizing internal structures for diagnosis of a disease and its monitoring. These include Ophthalmoscope, Endoscope, Colposcope and Dermatoscope.
Optical instruments are also used for precision and minimally invasive surgeries, including Laparoscope, Arthroscope and Surgical Microscopes.
Lasers are used for cutting, therapy and coagulation since they have precision and minimal invasiveness. CO? Laser, Excimer Laser and Fiber Optic Lasers are some of the optical instruments.
Optical instruments also help in monitoring vital signs in the body as well as for analysing biological samples. Pulse Oximeter, Spectrophotometer and Optical Coherence Tomography (OCT) are some of the optical instruments.
For cellular-level analysis and medical research, optical instruments like the Confocal Microscope and Fluorescence Microscope are used.
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