An object is 70 cm from a plano-convex lens whose curved side has curvature radius 29.5 cm. Th

An object is 70 cm from a plano-convex lens whose curved...

Key Concepts

Sign Conventions in Geometric Optics

Sign conventions are critical in optics for correctly interpreting distances and image types. They involve assigning positive or negative values to object distances, image distances, and focal lengths depending on the geometry of the lens and the direction of light travel, ensuring consistency in calculations.

Lens Maker's Formula

This concept relates the focal length of a lens to its refractive index and the radii of curvature of its surfaces. For a lens with one curved and one flat side, the formula simplifies and provides a way to calculate the focal length by considering the curvature of the lens surface that is curved, making it fundamental in lens design.

Thin Lens Equation

The thin lens equation (1/f = 1/do + 1/di) is essential for determining the relationship between object distance, image distance, and the lens's focal length. It is used to predict where an image will form and whether that image will be real or virtual, which is central to geometrical optics.

Focal Length

Focal length is the distance from the lens where parallel rays of light converge after passing through the lens (or appear to diverge from, in the case of a virtual image). It is a crucial parameter that governs the focusing properties of the lens and dictates the behavior of light passing through the lens.

Image Formation

Understanding how images are created by lenses involves knowing whether the image formed is real (can be projected on a screen) or virtual (cannot be projected), as well as whether it is magnified or reduced. This concept is fundamental to applications in optical instruments where the nature of the image determines usage.

Transcript

00:02 Problem 53.

00:04 An object is 70 centimeters from a plano -convax lens whose curved side has a radius of 29 .5 centimeters.

00:14 29 .5 centimeters.

00:16 The refractive index of the lens is 1 .63.

00:24 Where is the image and what type is it? so we have to use the lens maker's equation for this.

00:29 They do give us the object distance is 70 centimeters as well.

00:34 A plano convex lens has one curved side, which is convex, and one flat side.

00:41 So we use the lens maker's equation, which is 1 over f is n minus 1 times 1 over r1 minus 1 over r2.

00:54 And r1 would be the first curve surface, which is convex, if we have an object over here.

01:01 The first curved surface is convex to the object, so this will be a positive 29 .5.

01:06 I'll just plug numbers in as we find them, centimeters.

01:12 And r2, because this is flat, r2 is infinity.

01:17 It's not curved.

01:18 So r1 is 29 .5, and r2 is an infinite value.

01:24 And then n -1, they give us the index of a fraction of the substance, which would be the index of this year, and then 1 is the index of refraction of air.

01:33 So 1 .63 minus 1 is in front of that other term, and that's divided by, i mean, that's equal to 1 over the focal length.

01:44 So 1 over infinity is zero, essentially...

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