Chapter #19 Solutions - Introduction to Optics - Leno M Pedrotti, Leno S Pedrotti, Frank L Pedrotti - 3rd Edition

 

1. a. A 50-mW He-Cd laser emits at 441.6 nm. A 4-mW He-Ne laser emits at 632.8 nm. Using Figure 19-2, compare the relative brightness of the two laser beams of equal diameter when projected side by side on a white piece of paper. Assume photopic vision.b. What power argon laser emitting at 488 nm is required to match the brightness of a 0.5-mW He-Ne green laser at 543.5 nm under the conditions of (a)? Get solution

2. A lamp located 3 m directly above a point P on the floor of a room produces at P an illuminance of 100 lm/m2.a. What is the luminous intensity of the lamp?b. What is the illuminance produced at another point on the floor, 1 m distant from P? Get solution

3. A driveway is illuminated at night by identical lamps at the top of two poles 30 ft high and 40 ft apart. Assuming the lamps radiate equally in all directions, compare the illuminance at ground level for points directly under one lamp and midway between them. Get solution

4. A small source of 100 cd is situated at the focal point of a spherical mirror of 50-cm focal length and 10-cm diameter. What is the average illuminance of the parallel beam reflected from the mirror, assuming an overall reflectance of about 80%? Get solution

5. a. The sun subtends an angle of 0.5° at the earth’s surface, Where the illuminance is about 105 lx at normal incidence. Determine the luminance of the sun.b. Determine the illuminance of a horizontal surface under a hemispherical sky with uniform luminance L. Get solution

6. A circular disc of radius 20 cm and uniform luminance of 105 cd/m2 illuminates a small plane surface area of 1 cm2, 1 m distant from the center of the disc. The small surface is oriented such that its normal makes an angle of 45° with the axis joining the centers of the two surfaces. The axis is perpendicular to the circular disc. What is the luminous flux incident on the small surface? Get solution

7. Reference to Table 19-2 indicates that the corneal radius of curvature for the unaccommodated schematic eye is 8 mm. Treating the cornea as a thin surface (whose own refraction can be neglected), bounded by air on one side and aqueous humor on the other, determine the refractive power (see Section 2-10) of the corneal surface. Get solution

8. Consider the unaccommodated crystalline lens of the eye as an isolated unit having radii of curvature and effective refractive index as given for the schematic eye in Table 19-2.a. Calculate its focal length and refracting power as a thin lens in air.b. Calculate its focal length and refracting power in its actual environment, surrounded on both sides with fluid of effective index 1.33. Assume a thin lens.c. Calculate its focal length and refracting power again by treating it as a thick lens of thickness 3.6 mm. (The matrix techniques of Chapter 18 may well be applied to this problem). Get solution

9. Taking values for refractive indices and separation of elements from the schematic of the unaccommodated eye given in Table 19-2 and Figure 19-3, determine the distance behind the cornea where an image is focused for (a) an object at infinity and (b) an object at 25 cm from the eye. Use the Gaussian formula for image formation by a spherical surface in a three-step chain of calculations. In part (b), assume that the fully accommodated eye differs in the following ways: The front surface of the lens is more sharply curved, having a radius of +6 mm, but the back surface remains at −6 mm. As a result, the thickness of the lens along the axis increases to 4.0 mm, and the distance from cornea to the front surface of lens is shortened to 3.2 mm. Get solution

10. Use the matrix approach of Chapter 18 to find the system matrix for the unaccommodated schematic eye of Table 19-2 and Figure 19-3.a. Determine the four matrix elements of the system matrix where the system extends from the first refraction at the cornea to the final refraction at the second lens surface.b. From the matrix elements, determine the first and second focal points and the first and second principal points relative to the corneal surface. Compare with the distances given in Figure 19-3. Get solution

11. You have been asked to design a Snellen eye chart for a test distance of 5 ft. The chart is to include rows of letters to test for visual acuities of 20/300 (same as 5/75), 20/100, 20/60, 20/20, and 20/15, Determine the size of the block letter and letter detail (in inches) for each row of letters. Get solution

12. A presbyopic eye has no astigmatism, a near point of 125 cm, and a far point of infinity. Correction, with glasses using a lens placed 1.5 cm from the eye, requires that this person see objects at the normal near point (25 cm) clearly.a. What is the power of the corrective lens?b. With the lens of part (a), what is the far point of the corrected eye? Get solution

13. One eye of a person has a far point of 50 cm and a near point of 15 cm.a. What power contact lens is needed to correct the far point of this eye?b. Using the contact lens, what is the new near point of this eye?c. Repeat parts (a) and (b) if the corrective lens is a spectacle lens placed 2 cm from the eye. Get solution

14. Consider each of the following spectacle prescriptions and describe the refractive errors that are involved:a. −1.50, −1.50, axis 180b. −2.00c. +2.00d. +2.00, −1.50, axis 180 Get solution

15. Consider a woman with two myopic eyes. The vision in the woman’s left eye is corrected with a contact lens of power −7 diopters, and the vision in this woman’s right eye is corrected with a contact lens of power −5 diopters. The corrected near point of each eye is 15 cm and the corrected far point of each eye is infinity.a. Find the near and far points for each unaided eye.b. Suppose this woman mistakenly puts the right contact lens in her left eye and the left contact lens in her right eye. What are the near and far points of each eye when wearing the wrong corrective lens? Get solution

16. Consider a myopic, presbyopic eye with a near point of 13 cm and a far point of 15 cm. Design bifocals that will allow this person to see clearly both faraway objects and objects at a comfortable reading distance from the eye. Get solution


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