Mirror Equation Practice Problems

You hold a 5 cm tall bolt in front of a mirror. You observe a upright image located behind the mirror that is 2.5 cm tall in length. The distance between the image and object is 90 cm. Determine what the mirror's focal length will be.

Imagine a mirror is covered with a plano-concave glass, as shown in the figure below. The mirror and the curved surface of the glass both have the same radius of curvature. Consider a sphere, that is modeled like a point object, is placed outside the glass. Determine what the image distance formed by the mirror will be when measured from the mirror's surface.

A dressing room contains two nearly parallel mirrors separated by a distance of 4.0 m. A person stands 1.5 m away from the front of the mirror to view their reflection. Their back side reflects from the other mirror behind them so they can view it in mirror located in front of them. Therefore, they are able to first see their front side and then their backside reflection. Ideally, the parallel mirrors will produce one image only. Nevertheless, we can still model these particular mirrors to be parallel for the case of this problem. Determine what the distance between the person and their backside image will be.

A person doing their daily facial routine applying products on their face would like to view a reflection of their face that is magnified by 1.6 when their face is located 2.0 cm away from the mirror. Specify if the mirror used is convex or concave and determine what the mirror's focal length will be.

A student would like to measure the radius of curvature for a concave lens. The lens being studied does not transmit 100% of the light falling on it. Since light is reflecting from one side of the lens, a student is therefore able to treat the lens like a convex mirror. The student uses a square ring that is located 5.6 cm in front of the lens as an object. The student looks through the center of the square and places a ruler behind the lens in order to measure the size of the virtual image that is produced. The student determines that the magnification of the image is 0.052. Determine what the magnitude of the radius of curvature for this particular lens will be.

A burning gas lighter is located 1.50 m away from a projector screen. A geometric optics student selects a lens that has a focal length of 0.200 m to focus light from the gas lighter onto the projector screen. What are the distance(s) of this particular lens from the gas lighter that will lead to the formation of a sharper image produced on the projector's screen? Specify if the image is erect or inverted.

A concave spherical mirror of radius R is held in a transparent liquid medium of refractive index n. Calculate the focal length of the mirror in the liquid medium.

A grasshopper of height 1.0 cm sits at 14.0 cm on the left side of a concave spherical mirror. The magnitude of the radius of curvature for the mirror is 20.0 cm. Find (i) the position and (ii) the size of the grasshopper image. iii) Specify the characteristics of the image.

A scale model car is placed 15.0 cm to the left of the center of a reflective sphere. The radius of the sphere is 8.0 cm. i) Determine where the car image is located. ii) Calculate the magnification factor, m.

During a shot put competition, an athlete maintains the shot, a metal spherical ball of 12.0 cm in diameter, 20.0 cm from a cup placed on the bench. Determine the position of the cup's image with respect to the surface of the ball facing the cup.

A very small round object is placed 3.0 cm away from a concave dentist's mirror with a radius of curvature of 9.0 cm. Find the image distance from the mirror vertex. Is that image virtual?

A student would like to get a virtual image three times larger than the size of a penny. The student placed the penny 5 cm away from a concave mirror with a focal length of f. What should be the focal length, and the radius of curvature of the mirror in order to satisfy the student requirements?

A 0.5-mm-tall ant is situated along the principal axis of a thin, spherical shell of quartz coated with aluminum. The ant is 7.0 cm away from the mirror vertex, as shown in the image. The shell has a radius of 8.0 cm. i) Locate and ii) calculate the height of the ant's image.

An object needs to produce an image at infinity when reflected off a concave mirror with a radius of curvature equal to 50 cm. Where should this object be positioned?

When an object is placed 6 meters from a concave mirror, it results in an image with a lateral magnification of -0.8. What would be its focal length?

A makeup artist is getting ready for a busy day and needs a small mirror that can create an upright image magnified 2.5 times when positioned 1.50 cm from the face of her clients. What kind of mirror is best suited for her needs, and what should its radius of curvature be?

A distant mountain peak forms an upright and diminished virtual image located 20 cm behind a curved reflective surface. What kind of reflective surface could this be, and what would be its focal length?

In a small toy store, a customer is trying to create a fun display for kids using a toy car. The toy car has a height of 3.8 cm and is positioned 25 cm away from a spherical mirror. The customer wants to achieve an erect, virtual image of the car that measures 3.0 cm in height. (i) What type of mirror would the customer need to produce such an erect, virtual image? (ii) Where will this new image of the toy car form relative to the mirror? (iii) What is the focal length of the mirror required for this scenario? (iv) What could be the radius of curvature of this mirror?

Consider a concave mirror with a focal length of 15 cm. (i) At what distance from this mirror must an object lie so that its image forms on top of it? (ii) Is such a formed image considered real or virtual? (iii) Will such an image appear upside down or right side up? (iv) Calculate the magnification of the image.