Lens concepts

Light and Vision

Simple Magnifier

The simple magnifier achieves angular magnification by permitting the placement of the object closer to the eye than the eye could normally focus. The standard close focus distance is taken as 25 cm, and the angular magnification is given by the relationships below.

This precision magnifier performs the role of a simple magnifier, but has multiple elements to overcome aberrations and give a sharper image. Lens combinations are used to make high quality magnifiers for use as eyepieces.

Water droplet as a simple magnifier.

Water Droplet as a Simple Magnifier

A water droplet can act as a simple magnifier and magnify the object behind it. Water tends to form spherical droplets under the influence of surface tension. When attached to an object like these examples, the spherical shape is distorted, but still capable of forming an image. Above the droplets are on tiny emerging pine cones. At left the droplet forms a partial image of the flower that is out of focus behind it.

Refraction by a Convex Lens

Refraction bends the light downward upon entering the glass because the bottom part of the ray hits the slow medium first.

Light travels more slowly in glass than in air. The amount of bending depends upon the index of refraction of the glass.

Image formation depends upon bending light rays with lenses.

Refraction bends the light downward again upon leaving the glass because the top part of the ray hits the faster medium first.

Magnification:Transverse &Angular

The linear magnification or transverse magnification is the ratio of the image size to the object size. If the image and object are in the same medium it is just the image distance divided by the object distance.

Using the Gaussian form of the lens equation, a negative sign is used on the linear magnification equation as a reminder that all real images are inverted. If the image is virtual, the image distance will be negative, and the magnification will therefore be positive for the erect image.

If the media are different on the two sides of the surface or lens, the magnification is not quite so straigtforward. It can be variously expressed as

In this equation V is the vergence, n is the index of refraction, and u is used for the angle. Note that in this expression for the magnification, the minus sign doesn't appear. In this type of setting, the Cartesian sign convention is typically used and the object distance has a negative value. That takes care of the minus sign that is put in above in the Gaussian form.

The angular magnification of an instrument is the ratio of the angle subtended at the eye when using the instrument divided by the angular size without the instrument. An important example is the simple magnifier. The angular magnification of any optical system can be obtained from the system matrix for the system.

맺힌 상의 거리 구하기

물체의 렌즈로부터의 거리 p, 상의 렌즈로부터의 거리 i, 렌즈의 초점거리 f사이에는 다음과 같은 간단한 공식이 성립합니다.

p: 렌즈에서 물체까지의 거리 i: 렌즈에서 상까지의 거리 f: 초점 거리	오목렌즈의 경우 p > 0: 실물체 i < 0: 허상 (V쪽) f < 0: 허초점 (V쪽)
	볼록렌즈의 경우 p > 0: 실물체 i = ?: 상황에 따라 다르다. p < f 인 경우: i < 0 (정립 허상) p = f 인 경우: i 값을 구할 수 없다. p > f 인 경우: i < 0 (도립 실상) f > 0: 실초점 (R쪽)

배율 구하기

렌즈에 맺힌 상의 크기 비율도 구할 수 있습니다.

m: 배율 i: 렌즈에서 상까지의 거리 p: 렌즈에서 물체까지의 거리	m > 0: 상은 똑바로 서 있다. m < 0: 상은 뒤집혀 서 있다. |m| > 1: 상은 확대되어 있다. |m| < 1: 상은 축소되어 있다.

곡면거울의 경우와 별 차이가 없습니다.