Chapter 35: Optical Instruments

A microscope with a tube length of $180mm$achieves a total magnification of $800X$with a $40X$objectives and a $20X$eye piece. The microscope is focused for viewing with a related eye. how far is the sample from the objective lens?

A red card is illuminated by red light. What color will the card appear? What if it’s illuminated by blue light?

A $2.0cm$-tall object is $20cm$to the left of a lens with a focal length of$10cm$. A second lens with a focal length of$5cm$is $30cm$to the right of the first lens.

a. Use ray tracing to find the position and height of the image. Do this accurately using a ruler or paper with a grid, then make measurements on your diagram.

b. Calculate the image position and height. Compare with your ray-tracing answers in part a.

Modern microscopes are more likely to use a camera than human viewing. This is accomplished by replacing the eyepiece in Figure 35.14 with a photo-ocular that focuses the image of the objective to a real image on the sensor of a digital camera. A typical sensor is 22.5 mm wide and consists of 5625 4.0@mm@ wide pixels. Suppose a microscopist pairs a 40* objective with a 2.5* photo-ocular.

a. What is the field of view? That is, what width on the microscope stage, in mm, fills the sensor?

b. The photo of a cell is 120 pixels in diameter. What is the cell’s actual diameter, in mm?

Mordern microscopes are more likely to use a camera than human viewing. This is accomplished by replacing the eyepiece in figure $35.14$with a photo-ocular that focuses the image of the objectives to a real image on the sensor of a digital camera. A typical sensor is $22.5mm$wide and consists of $56254.0\mu m$wide pixels. suppose a microscopist pairs a $40X$objectives with a $2.5X$photo-ocular

a. what is the field of view? That is what width on the microscope stage in $mm$fills the sensor?

b. The photo of a cell is $120pixels$in a diameter. what is the cell's actual diameter in$\mu m$?

White light is incident onto a $30°$prism at the $40°angle$shown in Figure $p35.41$. Violet light emerges perpendicular to the rear face of the prism. The index of refraction of violet light in this glass is $20\%$larger than the index of refraction of red light. At what $angle\varphi$does red light emerges from the rear face?

White light is incident onto a $30°$prism at the $40°$angle shown in $figurep35.41$. violet light emerges perpendicular to the rear face of the prism. The index of refraction of violet light in this glass is $2.0\%$larger than the index of refraction of red light. At what angle does red light emerges from the rear face?

A beam of white light enters a transparent material. Wavelengths for which the index of refraction is n are refracted at angle u2. Wavelengths for which the index of refraction is n + dn, where dn V n, are refracted at angle u2 + du.

a. Show that the angular separation of the two wavelengths, in radians, is du = -1dn/n2 tan u2.

b. A beam of white light is incident on a piece of glass at 30.0°. Deep violet light is refracted 0.28° more than deep red light. The index of refraction for deep red light is known to be 1.552. What is the index of refraction for deep violet light?

High-power lasers are used to cut and weld materials by focusing the laser beam to a very small spot. This is like using a magnifying lens to focus the sun’s light to a small spot that can burn things. As an engineer, you have designed a laser cutting device in which the material to be cut is placed 5.0 cm behind the lens. You have selected a high-power laser with a wavelength of 1.06 mm. Your calculations indicate that the laser must be focused to a 5.0@mm@diameter spot in order to have sufficient power to make the cut. What is the minimum diameter of the lens you must install?

High-power lasers are used to cut and weld materials by focusing the laser beam to a very small spot. This is like using a magnifying lens to focus the sun light to a small spot that can burn things. As an engineer you have designed a laser cutting device in which the material to be cut is placed $5.0cm$behind the lens. you have selected a high-power laser with a wavelength of

your calculation indicates that the laser must be focused to a $5.0-\mu m-diameter$spot in order to have sufficient power to make the cut. what is the minimum diameter of lens you must install?