One night you are watching a movie with your significant other, who has 20/20 vi

Question

One night you are watching a movie with your significant other, who has 20/20 vision. You know that he/she likes to read the subtitles, which are 0.25 inches in height. The TV is 43 inches wide and the subtitles start and end 1 inch from each edge of the screen. What is the maximum distance you can have the couch (its center) from the TV, while keeping all the subtitles readable for your significant other? Assumptions: His/her eyes will be the same distance away from the screen as the couch. His/her eyes (and the center of the couch) will be aligned with the middle (width) of the TV screen and be level (in height) with the subtitles. Round to two decimal places.

Explanation / Answer

For a 20/20 vision, the visual angle for readable text is 5 minutes of arc
i.e visual angle, theta = 5/60 degrees
now, this angle, like the concept of pinhole cameras is related to the distance of the retina from the eyelens, and the height of the image formed at the retina

this angle is also related to thje distance of the object from the ey and its actual height
so, thius relatin is defined as
theta = h/D, theta in radians
where h is height of the object, D is its distance from the eye, and this relation is true only for small value of theta < 10 deg

so, theta = 5*pi/60*180 radians = 0.25/D [ given h = 0.25]
hence D = 171.887 in = 14.32 ft

hence the TV can be at a maximum distance of 14.32 feet from the couch

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.