Lab 11 Spherical Mirrors and Lenses PDF

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Spherical mirrors and lenses

Course: PHY156 Section: 12919

Student Name: Gamoi Paisley Lab Partner: Sarahi Marquez, Emmanuela Tanis

Date: 11/28/2017

Objective: To study the propagation of light reflected from spherical mirrors and light passing through spherical lenses and to determine the focal distance of spherical mirrors and lenses. Physical Principle: The shape and refracting properties of mirrors and lenses allows them to be able to form images of objects placed in front of them. There are two types of mirrors and lenses, one converts initially parallel light rays into converging rays and are known as concave mirrors and converging lenses, while the second type converts initially parallel light rays to diverging rays and are known as convex mirrors and diverging lenses. The simplest mirrors and lenses working as converging and diverging optical elements are those with spherical surfaces. When parallel rays hit a spherical concave mirror, upon reflection the rays converge and pass through the point which is known as the focal point. Since real light rays merge at this point, the focal point of concave mirrors is termed as the real focal point. If the mirror is convex, the initially parallel light rays diverge upon reflection and do not cross each other. However, a virtual extension of the rays to the back of the mirror will merge at the focal point. This point of concentration of virtual rays is known as the virtual focal point of convex mirrors. The distance between the focal point and the center of the mirror is the focal length ( f). The focal length is measured along the principal/optic axes of the mirror, which passes through the vertex and is the perpendicular bisector of the mirror. For any spherical mirror, the focal length is half of the radius of curvature of the mirror.

f=

R 2

Equipment:

       

Laser Ray Box Diverging and Converging Lenses 3-Sided Mirror (Plane, Convex and Concave) Ruler, Fine Point Pencil Masking Tape 11x14 Paper LED Lamp Clear Water

Procedure: Focal Point, Focal Length and Radius of Curvature of a Concave Mirror A sheet of paper was first taped to the desk. The ray box was then set to produce three rays and the center ray aligned on a line drawn on the paper. The mirror was then placed in the path of the rays and aligned so that the rays strikes the concave side. The mirror was again adjusted so that the middle ray strikes its vertex (center) and reflects back on itself. The position of the mirror was then traced, and the ray box adjusted so that the reflected rays intersect in the principal axis. This point of intersection was then labeled, and the path of the rays plotted. The ray box was then set to produce a single ray which

was then aligned so that it struck the mirror at some point far from its vertex. The direction of the ray was then adjusted so that the it reflects back on itself. The path of the ray was then plotted and the point at which it makes contact with the principal axis marked as the center of curvature of the mirror (C). The distance between the focal points (F) and the center of the mirror was then measured followed by the distance between the center of curvature and the center of the mirror. Focal Point, Focal Length and Radius of Curvature of a Convex Mirror The above procedure was repeated using the convex side of the mirror and the incident and reflected rays traced. The mirror was then removed, and the reflected rays reflected behind the mirror. The position at which these extended rays intersect on the principal axis was marked as the focal point of the mirror. A single ray was then drawn away from the vertex and the point of intersection with the principal axis marked as the center of curvature.

Focal Point and Focal Length of a Converging Lens A new sheet of paper was then placed on the table with a line which represents the principal axis of the lens. A converging lens was then placed in the middle of the axis and was positioned perpendicular to it. The ray box was then set to produce three parallel rays which were then aimed towards the lens with the center ray aligned along the principal axis. The initial and transmitted rays along with the position of the lens was then traced and the point at which the transmitted rays converge on the principal axis noted as the first focal point of the lens ( F1). The procedure was then repeated on the opposite side of the lens and the second focal point labeled (F2). The lens was then removed and the center of the lens marked on the principal axis. The distance between this point and the focal points measured f1 and f2.

Lab Data: Please see the attached data sheets.

Calculations: Focal Point, Focal Length and Radius of Curvature of a Concave Mirror R = 11.1cm

f = 5.4cm

R 11.1 f calc .= = =5.55 cm 2 2 ¿ 5.40−5.55 ∨ ¿ ×100=2.7 % 5.55 ¿ f measured −f calc .∨ ¿ ×100=¿ f calc . %Diffefence=¿

Focal Point, Focal Length and Radius of Curvature of a Convex Mirror

R = 11.1cm

f = 4.8cm

R 11.1 =5.55 cm f calc .= = 2 2 ¿ 4 .8 0−5.55∨ ¿ × 100=13.5 % 5.55 ¿ f measured −f calc .∨ ¿ ×100=¿ f calc . %Diffefence=¿

Focal Point and Focal Length of a Converging Lens f1 = 8.35cm

f2 = 8.6cm

¿ 8.60− 8.35∨ ¿ × 100=3.0 % 8.35 ¿ f 2− f 1∨ ¿ ×100=¿ f1 %Diffefence=¿

Focal Point and Focal Length of a Diverging Lens f1 = 6.0cm

f2 = 6.2cm

¿ 6.2−6.0 ∨ ¿ ×100=3.3 % 6.0 ¿ f 2−f 1∨ ¿ × 100=¿ f1 %Diffefence=¿ Discussion: In this experiment, the propagation of light reflected from spherical mirrors and light passing through spherical lens was examined and their focal lengths determined. The radius of curvature of the concave mirror was found to be 11.1cm. This value was used to determine the theoretical focal length (5.55cm) using the appropriate formula. The measured focal length was found to be 5.4cm which was found to have a percentage difference of 2.7%. This error may have been due to systematic and gross errors which occurred throughout the experiment. The radius of curvature of the convex mirror was found to be 11.1cm. This value was used to determine the theoretical focal length (5.55cm) using the appropriate formula. The measured focal length was found to be 4.8cm which was found to have the largest experimental error of 13.5%. This error may have been due to systematic and gross errors which occurred throughout the experiment. The focal length of the converging lens was determined by measuring the distance between the focal point of the rays and the center of the lens. In theory, the focal length from both sides of lens should be equal, however f1 was round to be 8.35cm while f2 was found to be 8.60cm. This produced a percentage difference of 3.0% which may have been caused by errors which occurred throughout the experiment.

The focal length of the diverging lens was determined by measuring the distance between the focal point of the rays and the center of the lens. In theory, the focal length from both sides of lens should be equal, however f1 was round to be 6.0cm while f2 was found to be 6.2cm. This produced a percentage difference of 3.3% which may have been caused by errors which occurred throughout the experiment. This errors which occurred in this experiment may have been caused by gross errors when marking the position of the beam on the paper. The line may not have been traced at the center of the ray or the ruler may have not been aligned correctly then tracing the beams path. Also, the lens or mirror may have shifted while tracing the position of the beam. Systematic errors associated with each instrument used may have also contributed to these errors such as errors associated with the measurements on the ruler.

Conclusion: The focal lengths of a concave mirror, convex mirror, converging lens and diverging lens was successfully determined experimentally.

Answers to Questions: 1. Explain, why the center of curvature of a spherical mirror can be found using the rays reflected upon itself (see Procedure Parts I and II)? If an object is at the center of a spherical mirror, the reflected light will also pass through the center of sphere. Therefore the point at which a beam of light becomes reflected upon itself can be used to determine the center of curvature along a known axis. 2. Which mirrors can be used for projecting images on a screen? Both convex and concave mirrors can be used to project an image onto a screen, however a lens may be needed to focus the image. 3. Which lenses can be used for projecting images on a screen? A converging lens can be used to project an image on to a screen since it will be at focus in front of the lens while a diverging lens would not be in focus in front of the lens. 4. Which mirrors and lenses can produce real images? Under which conditions? A real image is produced when an object is at a distance greater than the focal length, concave mirrors converging lenses are able to produce real images 5. Which mirrors and lenses can produce virtual images? Under which conditions? Convex mirrors and diverging lenses always produce virtual images since the reflected or transmitted rays do not meet at the focal point. Concave mirrors are also able to form virtual images if the ovject is at a distance less than the focal length....