9.32 Figure 9.34 shows an equiconvex lens (of refractive index 1.50) in contact with a liquid layer on top of a plane mirror. A small needle with its tip on the principal axis is moved along the axis until its inverted image is found at the position of the needle. The distance of the needle from the lens is measured to be 45.0 cm. The liquid is removed and the experiment is repeated. The new distance is measured to be 30.0 cm. What is the refractive index of the liquid?
The liquid acts as a mirror, focal length of the liquid =
Focal length of the system (convex lens + liquid), = 45 cm
For a pair of optical systems placed in contact, the equivalent focal length is given as
= + or = -
- 90 cm
Let the refractive index of the lens be and the radius of curvature of one surface be R
Hence, the radius of curvature of the other surface is –R
R can be obtained by using the relation
= ( + ) = (1.5 – 1)(
= ,
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9.32 Focal length of the convex lens, = 30 cm
The liquid acts as a mirror, focal length of the liquid =
Focal length of the system (convex lens + liquid), = 45 cm
For a pair of optical systems placed in contact, the equivalent focal length is given as
= + or = -
- 90 cm
Let the refractive index of the lens be and the radius of curvature of one surface be R
Hence, the radius of curvature of the other surface is –R
R can be obtained by using the relation
= ( + ) = (1.5 – 1)(
= , so R = 30 cm
Let the refractive index of the liquid be
The radius of curvature of the liquid on the side of the plane mirror =
Radius of curvature of the liquid on the side of the lens, R = -30 cm
The value of can be calculated using the relation,
= ( - )
= ( - 0)
- 1 =
= 1.33
Hence, the refractive index of the liquid is 1.33.
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<p><strong>9.32 </strong>Focal length of the convex lens, <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> = 30 cm</p><p>The liquid acts as a mirror, focal length of the liquid = <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></p><p>Focal length of the system (convex lens + liquid), <span title="Click to copy mathml"><math><mi>f</mi><mi></mi></math></span> = 45 cm</p><p>For a pair of optical systems placed in contact, the equivalent focal length is given as</p><p><span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mi>f</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>1</mn></mrow></mrow></msub></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><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>f</mi></mrow></mrow></mfrac><mo>-</mo><mi></mi><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><msub><mrow><mrow><mi>f</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></mrow></mrow></mfrac></math></span> = <span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mn>45</mn></mrow></mrow></mfrac></math></span> - <span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mn>30</mn></mrow></mrow></mfrac></math></span></p><p><span title="Click to copy mathml"><math><msub><mrow><mrow><mi>f</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub><mo>=</mo><mi></mi></math></span> - 90 cm</p><p>Let the refractive index of the lens be <span title="Click to copy mathml"><math><msub><mrow><mrow><mi>μ</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></math></span> and the radius of curvature of one surface be R</p><p>Hence, the radius of curvature of the other surface is –R</p><p>R can be obtained by using the relation</p><p><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>1</mn></mrow></mrow></msub></mrow></mrow></mfrac></math></span> = ( <span title="Click to copy mathml"><math><msub><mrow><mrow><mi>μ</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub><mo>-</mo><mi></mi><mn>1</mn><mo>)</mo><mo>(</mo><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mi>R</mi></mrow></mrow></mfrac></math></span> + <span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mfenced open="|" close="|" separators="|"><mrow><mrow><mi>R</mi></mrow></mrow></mfenced></mrow></mrow></mfrac></math></span> ) = (1.5 – 1)( <span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>2</mn></mrow></mrow><mrow><mrow><mi>R</mi></mrow></mrow></mfrac><mo>)</mo></math></span></p><p><span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mn>30</mn></mrow></mrow></mfrac></math></span> = <span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mi>R</mi></mrow></mrow></mfrac></math></span> , so R = 30 cm</p><p>Let the refractive index of the liquid be <span title="Click to copy mathml"><math><msub><mrow><mrow><mi>μ</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></math></span></p><p>The radius of curvature of the liquid on the side of the plane mirror = <span title="Click to copy mathml"><math><mi>∞</mi></math></span></p><p>Radius of curvature of the liquid on the side of the lens, R = -30 cm</p><p>The value of <span title="Click to copy mathml"><math><msub><mrow><mrow><mi>μ</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></math></span> can be calculated using the relation,</p><p><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> = ( <span title="Click to copy mathml"><math><msub><mrow><mrow><mi>μ</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub><mo>-</mo><mi></mi><mn>1</mn><mo>)</mo><mo>(</mo><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mo>-</mo><mi>R</mi></mrow></mrow></mfrac></math></span> - <span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mi>∞</mi></mrow></mrow></mfrac></math></span> )</p><p><span title="Click to copy mathml"><math><mfrac><mrow><mrow><mo>-</mo><mn>1</mn></mrow></mrow><mrow><mrow><mn>90</mn></mrow></mrow></mfrac></math></span> = ( <span title="Click to copy mathml"><math><msub><mrow><mrow><mi>μ</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub><mo>-</mo><mi></mi><mn>1</mn><mo>)</mo><mo>(</mo><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mn>30</mn></mrow></mrow></mfrac></math></span> - 0)</p><p><span title="Click to copy mathml"><math><msub><mrow><mrow><mi>μ</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></math></span> - 1 = <span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></mfrac></math></span></p><p><span title="Click to copy mathml"><math><msub><mrow><mrow><mi>μ</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub><mo>=</mo><mi></mi><mfrac><mrow><mrow><mn>4</mn></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></mfrac></math></span> = 1.33</p><p>Hence, the refractive index of the liquid is 1.33.</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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