We now derive the mirror equation or the relation between the object distance u, image distance v and the focal length f. The centre of the square is at the axis of the mirror and the plane is normal to the axis. The derivation of equation 34 is straightforward, but a bit tedious. Derivation of lens formula concave lens let ab represent an object placed at right angles to the principal axis at a distance greater than the focal length f of the convex lens. Use the mirror equations to determine location, size, orientation, and nature of images formed with spherical. A mirror is a surface which reflects a clear image. Mirror formula for convex mirror when real image is formed let ab be an object lying beyond the focus of a concave mirror. A concave mirror is that spherical mirror in which the reflection of light. Focusing properties of spherical and parabolic mirrors 1. Physics notes for class 12 chapter 9 ray optics and. A ray parallel to mirror axis passes through the focal point of a concave mirror or appears to come from the focal point of a convex mirror. Derivation or proofofmirror formulax physics jsunil.
A spherical mirror is that mirror whose reflecting surface is the part of a hollow sphere of glass. So, go ahead and check the important notes for class 12 physics ray optics. The mirror formula is applicable both in plane mirrors and spherical mirrors convex and concave mirrors. This video is highly rated by jee students and has been viewed 29 times. We can define two general types of spherical mirrors. Derivation of mirror formula detailed mirror formula derivation. From the calculations in this problem it can be concluded that if a 4. This sign convention is known as new cartesian sign convention. Power of a convex lens is positive and that of a concave lens is negative. Mirror formula with solved numericals class 10 teachoo. I understand how this formula can be proved using a ray diagram for concave mirrors simply by proving similar triangles between the image distance and the object distance. Online physics calculator that calculates the concave mirror equation from the given values of object distance do, the image distance di, and the focal length f.
With spherical mirrors, reflection of light occurs at a. Thus, in this case, where is the focal length of the mirror, and eq. Candidates who are pursuing in class 12 are advised to revise the notes from this post. Mirror formula class 10, lightreflection and refraction. Its outer convex surface is polished and inner concave surface reflects.
Derivation or proofof the relation between focal length and radius of curvaturex physics r2f. Start with a curve, denoted by yx in the xy plane, that is symmetrical under a re. Question 5 write the mirror formula for a spherical mirror. The ray ab, after reflection from mirror will pass through f concave mirror or will appear to diverge from f convex mirror from the. How can geometry, algebra and simple ray construction be used with a concave mirror in order to develop a relationship between the object distance, image. A trucker sees the image of a car passing her truck in her diverging rearview.
Reflection and mirrors the following information is provided to the student. A convex mirror can only produce a virtual image since all reflected rays will diverge. Let ab be an object placed on the principal axis of a convex mirror of focal length f. With the help of notes, candidates can plan their strategy for particular weaker section of the subject and study hard.
A mirror whose surface is cut out of a spherical shell, is called a spherical mirror. Some terms related to spherical mirrors are given below i centre of curvature it is the centre of the sphere of which the mirror or lens is a part. In this video tutorial, we will learn the fundamental concepts of ray optics and understand how light is reflected, absorbed, and transmitted. Question 4 what are the sign conventions for concave mirror. A square of side 3 cm is placed at a distance of 25 cm from a concave mirror of focal length 10 cm. This expression relates the object distance, the image distance, and the radius of curvature of the mirror. A curved mirror is a mirror with a curved reflecting surface. Both equations are valid for concave and convex mirrors and for real and virtual images.
The position of the image is obtained by drawing a ray diagram. For the love of physics walter lewin may 16, 2011 duration. The mirror formula derivation is provided here so that. The most common nonspherical type are parabolic reflectors, found in optical devices such as reflecting telescopes that need. The surface may be either convex bulging outward or concave recessed inward. A ray of light bl after reflecting from the concave mirror passes through the principal axis at f and goes along lb. A mirror formula can be defined as the formula which gives the relationship between the distance of object u, the distance of image v, and the focal length of the mirror f. Focusing properties of spherical and parabolic mirrors. For an object which is very far away from the mirror i. Cbse notes class 12 physics ray optics aglasem schools. Derivation of the mirror equation video khan academy. Derivation for magnification equation for convex mirrors. If the reflecting surface is the outer side of the sphere, the mirror is called a convex mirror. Derivation of mirror formula detailed mirror formula.
If the inside surface is the reflecting surface, it is called a concave mirror symmetry is one of the major hallmarks of many optical devices, including mirrors and lenses. The area enclosed by the image of the square is a 4 c m 2 b 6 c m 2 c 16 c m 2 d 36 c m 2. The yaxis is thus the symmetryaxis of the twodimensional. From the calculations in the second sample problem it can be concluded that if a 4. I also know that spherical mirrors experience spherical aberration, and. Our mission is to provide a free, worldclass education to anyone, anywhere.
Consider a convex lens or concave lens of absolute refractive index m 2 to be placed in a rarer medium of absolute refractive index m 1 considering the refraction of a point object on the surface xp 1 y, the image is formed at i 1 who is at a distance of v 1 ci 1 p 1 i 1 v 1 as the lens is thin. Whenever a light ray hits the interface between two. As a demonstration of the effectiveness of the mirror equation and magnification equation, consider the following example problem and its solution. A ray of light starting from the end point a of the object and moving parallel to the principal axis strikes the mirror at the point e. After reflection from the mirror, the ray appears to come from focus f. The power of a lens is defined as the reciprocal of its focal length. For a convex mirror, prove that its focal length is equal. This derivation relies mostly on snells law and the smallangle approximation. Refractive index of a transparent liquid measured with a.
Cartesian sign convention for spherical mirror class 10. Concave mirror convex mirror image formation by concave mirror concave mirror ray diagram image formation by convex mirror. The mirror equation and magnification the two right triangles are similar in each case. An image which can be formed on the screen is known as real image and the one which cannot be formed on screen is known as a virtual image. How far behind the mirror does the candle appear, and how large is it. You got the approximate focal length of the concave mirror by measuring the distance of the image from the mirror. How can geometry, algebra and simple ray construction be used with a concave mirror in order to develop a relationship between the. Its inner concave surface is polished and outer convex surface reflects. Most curved mirrors have surfaces that are shaped like part of a sphere, but other shapes are sometimes used in optical devices. General considerations consider a curved mirror surface that is constructed as follows. Further information about the sign conventions for the variables in the mirror equation and the magnification equation can be found in lesson 3. Question 2 a concave mirror produces three times magnified real image of an object placed at 10cm in front of it.
Rays that hit far away from the principal axis will not obey this mirror equation very well. Concave mirror equation calculator calculate focal. It is converging to the point o, and, if the concave lens had not got in the way, it would have formed a real image at o. Relation between f and r for a convex mirrorif c is the centre of curvature, then pc r, is the radius of the curvature and cb is the normal to the mirror at. We will start with reflection of light and spherical mirrors and gradually proceed to cover advanced topics such as refraction, prisms, total internal reflection, and optical instruments. However, it didnt quite work out for the convex mirrors as i worked for a few days trying to identify a. Magnification produced by a lens is also related to the objectdistance u, and the imagedistance v and is given by.
The figure shows an object ab at a distance u from the pole of a concave mirror. Sign is taken as negative from pole of a spherical mirror towards object along the principal axis. In the case of spherical mirror all signs are taken from pole of the spherical mirror, which is often called origin or origin point. The image a 1 b 1 is formed between o and f 1 on the same side as the object is kept and the image is erect and virtual. The power p of a lens of focal length f is given by. Mirror equation minus since inverted magnification equation consider the real image produced from a concave mirror. To create a real image with a concave mirror, the object must be outside the focal point. Image formation by concave mirrors university of texas. The image a 1 b 1 is formed at a distance v from the mirror.
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