11. The image of an object is located 6cm behind a convex mirror. If it's magnification is 0.6, calculate the focal length of the mirror.
12. A simple microscope forms an image 10cm from an eye close to the lens. If the object is 6cm from the eye. Calculate the focal length of the lens.
13. In a compound microscope, the image formed by the objective lens is at a distance of 3.0 cm from the eye lens. If the final image is at 25.0cm from the eye lens, calculate the focal length of the eye lens
14.A converging lens of focal length 15 cm forms a virtual image at a point 10cm from the lens. Calculate the distance of the object from the lens.
15. The distance between a concave mirror and an object placed Infront it is 1.0cm. if the radius of curvature of the mirror is 4.0, the image formed will be.
11. The mirror equation for a convex mirror is:
1/f = 1/v - 1/u,
where f is the focal length, v is the image distance, and u is the object distance.
In this case, the image distance v is given as 6 cm and the magnification is given as 0.6.
The magnification (M) is also given by the equation:
M = -v/u,
where the negative sign indicates that the image is inverted.
Substituting the given values into the equation, we have:
0.6 = -6/u.
Solving for u, we get:
0.6u = -6,
u = -6/0.6,
u = -10 cm.
Now we can substitute the values u = -10 cm and v = 6 cm into the mirror equation:
1/f = 1/6 + 1/10.
Simplifying the equation, we get:
1/f = 10/60 + 6/60,
1/f = 16/60,
f = 60/16,
f ≈ 3.75 cm.
Therefore, the focal length of the convex mirror is approximately 3.75 cm.
12. The magnification (M) for a simple microscope is given by the equation:
M = -v/u,
where v is the image distance and u is the object distance.
In this case, the image distance v is given as 10 cm and the object distance u is given as 6 cm.
Substituting the values into the equation, we have:
0.6 = -10/6.
Solving for 0.6u = -10, we get:
0.6u = -10,
u = -10/0.6,
u = -16.67 cm.
Therefore, the focal length of the lens is approximately 16.67 cm.
13. The compound microscope consists of an objective lens and an eye lens. The total magnification (M_total) of the compound microscope is given by the product of the magnification of the objective lens (M_objective) and the magnification of the eye lens (M_eye):
M_total = M_objective * M_eye,
where M_objective = v_objective / u_objective and M_eye = v_eye / u_eye.
In this case, the image distance v_objective is given as 3.0 cm and the final image distance v_eye is given as 25.0 cm.
The magnification of the objective lens can be calculated using the lens formula:
1/f_objective = 1/v_objective - 1/u_objective.
The magnification of the eye lens can be calculated using the lens formula:
1/f_eye = 1/v_eye - 1/u_eye.
We need to find the focal length of the eye lens (f_eye).
Since we have both v_eye and v_objective, let's substitute the values into the lens formula for the eye lens:
1/f_eye = 1/25 - 1/3.
Simplifying the equation, we have:
1/f_eye = 1/75 - 1/3,
1/f_eye = (1 - 25)/75,
1/f_eye = -24/75,
f_eye = -75/24,
f_eye ≈ -3.13 cm.
Therefore, the focal length of the eye lens is approximately -3.13 cm.
14. The lens formula for a converging lens is:
1/f = 1/v - 1/u,
where f is the focal length, v is the image distance, and u is the object distance.
In this case, the focal length f is given as 15 cm and the image distance v is given as 10 cm.
Substituting the values into the lens formula, we have:
1/15 = 1/10 - 1/u.
Simplifying the equation, we get:
1/15 = (1 - 15)/10u,
1/15 = -14/10u,
10u = -14 * 15,
u = -210/10,
u = -21 cm.
Therefore, the distance of the object from the lens is -21 cm.
Note: The negative sign indicates that the object is located on the same side as the observer.
15. The focal length of a concave mirror is half the radius of curvature. In this case, the radius of curvature is given as 4.0 cm. Therefore, the focal length is half the radius of curvature, which is 2.0 cm.
If the distance between the concave mirror and the object placed in front of it is 1.0 cm, then the image formed will be real and located on the same side as the object. The exact position of the image can be determined using the mirror formula:
1/f = 1/v - 1/u,
where f is the focal length, v is the image distance, and u is the object distance.
Substituting the values into the formula, we get:
1/2 = 1/v - 1/1.
Simplifying the equation, we have:
1/2 = 1/v - 1,
1/2 = (1 - v)/v,
v = 2,
Therefore, the image formed is 2.0 cm from the concave mirror.