# Convex lens

## Difference

breeze lens, two-sided light, the refractive index is the same. The focal length is also the same.

flat convex lens, the light incident on both sides, the refractive index is slightly different. So the focal length in the actual on both sides is also different. When using it, it cannot be reversed.

## Effects

This type of lens is used to converge parallel light, or convert the point source into parallel light.

rationally select material (texture, bubbles, impurities, uniformity); when grinding, it does not produce disabled (scratches, dents, luster) when applying for interference light.

Specifications have no coating and a disproportionable multilayer film lens of visible optical belt domain.

Telescope:

In May 1609, the famous scientist garello visited Venice at the age of 45. There he heard the story of the Dutch to make a telescope and excited for this.

Galileo immediately creates his own telescope. He installed a flat convex lens and a flat concave lens at both ends of a lead tube. The flat concave lens is close to one end of the eye, called a eyepiece. The flat convex lens is close to the end of the observation, called an objective lens. When he uses a homemade telescope to observe the object, the distant object is amplified many times.

Galileo is not the first inventive telescope, but becomes the first person who is the first to give a telescope. Since then, the astronomical telescope is born. Astronomical has gained a new weapon for exploring the universe, and therefore achieved another amazing discovery.

## Calculation example

There is a focal length formula for a thickness flat lens

, for example: a thickness of 5, a flat convex lens having a radius of 20 (1) If the circle half of the convex lens plane:

1. The spherical half of the convex lens is calculated: R ^ 2 = 20 ^ 2 + (R-5) ^ 2, R = 42.5;

2. Do parallel the light axis line AA ', the convectance lens sphere on the point A, the straight line AA "is perpendicular to the optical axis, the intersection of the optical axis is A", the straight segment AA "is H, do line OA, FA, where O is the core, f is the focus, and the tangent AB of the convex lenticular sphere is performed. The vertical AB is perpendicular to the point B, and the line OA is the normal line AA ';

3 The sine value of the incident angle is calculated: since the AA 'parallel optical axis Of, the angle of incident angle A = ∠AOB, SIN (a) = sin (AOB) = H / R, ∠AOB = Arcsin (H / R);

4. The refractive index of the material used for the convex lens is N, and the sine value sin (b) = sin (a) / n = (h / r) / n = (h * n) / r SIN (OAF) = (h * n) / r, ∠OAF = arcsin [(h * n) / r];

5. ∠afo = ∠AOB-∠OAF = arcsin [ H * n) / r] -arcsin (h / r), TG (AFO) = Tg {Arcsin [(h * n) / r] -arcsin (h / r)} = aa "/ fa" = h / fa ", Fa" = h / tg {Arcsin [(h * n) / r] -arcsin (h / r)};

6. One side is a flat thin convex lens, the optical center can be approximately considered It is the center of the plane, so the focal length f = Of + (R-5) = (FA "-oa") + (R-5), and OA ^ 2 = OA "^ 2 + aa" ^ 2, ie OA "= √ (OA ^ 2-aa "^ 2) = √ (R ^ 2-h ^ 2);

7. Finally, put the FA", OA "into, simplifying the calculation can calculate the focal length f

(2) If the ball radius of the convex lens, the first step in the above step may be omitted, and it will be done directly from the second step.

## Curvature radius / h2>

Newton ring is composed of a flat glass sheet to be tested (about 200 to 700 cm) and the polished radius of convex lenses and the polished flat glass plate, which is a flat convex lens with a large radius of curvature When the convex surface is in contact with a wear light flat glass plate, a gas film, a distance from the contact point, the same distance is the same, and the thickness is the same. If the thickness is the same as a monochrome parallel light of a wavelength λ Based on this device, the optical wave reflected by the upper and lower surface of the air film will interfere with each other, and the interference stripe is the trajectory of the contrast of the film, such interference is an equal thick interference.

When viewed in the reflection direction, a set of circular interference stripes between bright and dark in contact points is seen, and the center is a dark spot. If it is observed in the lens direction, the interference ring and reflected light The optical strength distribution of the interference ring is complementary, the center is a bright spot. The original bright ring becomes a dark ring, and the dark rings become bright rings. This interference phenomenon is the earliest of Newton. It is called Newton ring.

### principle

1, Newton ring

Newton ring is a flat convex lens (about 200 to 700 cm of convex curvature) L and polished The flat glass plate P laminated in the metal frame f. Figure 1. There are three spiral h on the side of the frame to modulate contact between L and P to change the shape and position of the interference ring. When adjusting h, the spiral is not rotated too tight to prevent the contact pressure excessively caused by lens elasticity and even damage the lens.

When the convex surface of a flat convex lens with a large radius of curvature is in contact with a mood, the convex surface and the flat glass plate will form a air film, the contact point is equal to the direction. Place, the thickness is the same. as shown in picture 2. If the monochrome parallel light is from the wavelength of λ to such a device, the optical wave reflected by the upper and lower surface of the air film will interfere with each other, and the interference stripe is the trajectory of the thickness of the film, which is a kind of interference. Equal thick interference.

When viewing in the reflection direction, a set of circular interference stripes between bright and dark in contact point is seen, and the center is a dark spot (Fig. 3 (a)) if in the lens When the direction is observed, the light intensity of the interference ring of the interference loop and the reflected light is complementary, the center is a bright spot, the original bright ring becomes a dark ring, and the dark ring becomes bright ring (Figure 3 (B) This interference phenomenon is the earliest of Newton, so it is called Newton.

The radius of curvature of the lens L is R, the radius of the formed M-stage interference dark stripe is

, and the formed M-level interference bright stripe is
, It is not difficult to prove the picture.

The above two shows that when λ is known, the radius of the lens can be calculated from the radius of the first M-level dark ring (or bright ring), which is opposite, when R is known, Λ can be calculated. However, since the two contact mirrors are inevitably attached to the dust, it is inevitable that the elasticity is changed during contact, so that the contact may not be a geometric point, but a circular spot, so the circular circle is relatively blurred and wide, so it is difficult to It is not certainly determined that the number of interference grade M, that is, the number of stages and orders of the interference ring is not necessarily consistent. This can only have a large error if only one loop radius is measured. In order to reduce the error, improve the measurement accuracy, it is necessary to measure the radius of two looped ribs from the center, more clearly, and measured the radius of m1 and M2 dark ring (or bright ring) (here M1, M2) Both of the ring sequence, not necessarily an interference grade number), and thus Figure 1 (1) should be corrected to

= (m + J) Rλ ------ (3)

Mi is the number of ring sequence, (m + j) is the number of interference grade (J is the interferometry), and is shown in FIG. 3 (4).

upper surface, the radius of the two rings and the number of interference stages and the number of ring sequence are independent, and only the difference between the number of the two rings (M2-M1). Therefore, as long as the radius of the two rings is accurately measured, the radius of the radius of the two loops can accurately calculate the radius of curvature R, i.e., (5) and (6) of Fig. 3, and (6).

### Supplement

By (3), you can know,

and M linear relationship, as shown in Figure 4, whose slope is Rλ, and therefore, a set of dark rings can also be measured (or Light ring) radius
and their corresponding ring sequence M, as the relationship curve of
---- m, then calculates R from the straight slope.

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