Geometrical Optics Test Quiz!

Explanation
The given equation xy=f2 represents the relationship between the distance of the object and the image formed by a concave mirror from its focus (x and y) and the focal length (f). This equation implies that the product of x and y is equal to the square of the focal length.

Explanation
When a double convex lens is cut into four equivalent parts, the focal length of each part becomes twice the original focal length. This is because cutting the lens into four parts results in each part having half the thickness of the original lens. According to the lens formula, the focal length is inversely proportional to the thickness of the lens. Therefore, when the thickness is halved, the focal length doubles. Hence, the correct answer is 2f.

Explanation
The given answer, (n - 1)f, is the correct option. In concave lenses, the image formed is always virtual, erect, and diminished. The magnification produced by a concave lens is given by the formula (1/n), where n is the refractive index of the medium surrounding the lens. The negative sign indicates that the image is inverted. The distance of the object from the lens is given by the focal length multiplied by (n - 1) according to the lens formula, which states that the reciprocal of the object distance plus the reciprocal of the image distance is equal to the reciprocal of the focal length. Therefore, the correct answer is (n - 1)f.

Explanation
When a thin convex lens forms a distinct image of an object on a screen, it means that the object is located at the focal point of the lens. In this scenario, the lens is initially placed at a distance of 30 cm from the screen, and the image is formed at this distance. When the lens is displaced 5 cm towards the screen, the screen also needs to be displaced 5 cm towards the lens to maintain the same distance between the lens and the screen. This displacement indicates that the new image is formed at a distance of 25 cm from the lens. Since the object is located at the focal point, the focal length of the lens is equal to the distance between the lens and the screen, which is 10 cm.

Explanation
When two lenses are in contact, the effective focal length of the combination can be calculated using the lens maker's formula. In this case, since the lenses are identical and equiconvex, their individual focal lengths would be the same, denoted as f.

When the lenses are in contact, the effective focal length is given by the equation:

1/f_effective = (ng - nw) * (1/R1 - 1/R2)

Since the lenses are identical, their radii of curvature (R1 and R2) would be the same. Therefore, the equation simplifies to:

1/f_effective = (ng - nw) * (2/R)

Since the lenses are in contact, the separation between them is negligible, so the value of R can be considered infinite. Therefore, 1/R is equal to zero.

Thus, the equation becomes:

1/f_effective = (ng - nw) * 0

This means that the effective focal length is also zero.

Therefore, the correct answer is 3f/4.

Explanation
The angle of minimum deviation for a prism is given by the equation D = A + A' - 180, where A is the angle of the prism and A' is the angle of deviation. In this case, the refracting angle of the prism is A, so the angle of deviation is A/2. Substituting these values into the equation, we get D = A + A/2 - 180 = 3A/2 - 180. Simplifying further, we get D = 180 - 2A, which matches the given answer of 1800 - 2A. Therefore, the correct answer is 1800 - 2A.

Explanation
When a thin prism of glass is placed in air, it produces a deviation of 40° in a light ray. The angle of deviation (ang) is given as 3/2. Now, if the same prism is placed in water, the angle of deviation (anw) is given as 4/3. Since the angle of deviation is directly proportional to the refractive index of the medium, we can use the formula: ang/angw = anw/a. By substituting the given values, we can find the new deviation in degrees. In this case, the new deviation would be 30°.

Explanation
When the space between the object and the objective of a microscope is filled with water, the resolving power of the microscope increases. This is because water has a higher refractive index compared to air, which allows for a shorter wavelength of light to be used. As the resolving power of a microscope is directly proportional to the wavelength of light used, using water as the medium increases the resolving power. This enables the microscope to distinguish finer details and improve the clarity of the observed image.

Explanation
The magnifying power of a compound microscope can be calculated using the formula: M = (1 + (D / fe)) * (D / f0), where M is the magnifying power, D is the least distance of distinct vision, fe is the focal length of the eyepiece, and f0 is the focal length of the objective. In this case, the distance between the objective and the real image is given as 18 cm, which can be considered as the least distance of distinct vision. The focal length of the eyepiece (fe) is given as 2.0 cm and the focal length of the objective (f0) is given as 0.4 cm. Plugging in these values into the formula, we get M = (1 + (18 / 2.0)) * (18 / 0.4) = 19 * 45 = 855. Therefore, the magnifying power is 855, which is not one of the given answer choices. Hence, the correct answer is -- 594.

Explanation
The magnifying power of an astronomical telescope is given by the formula: Magnifying power = focal length of objective / focal length of eyepiece. In this case, the magnifying power is given as 10 and the focal length of the objective is given as 1.20 m. Rearranging the formula, we can find the focal length of the eyepiece by dividing the focal length of the objective by the magnifying power. Therefore, the focal length of the eyepiece will be 1.20 m / 10 = 0.12 m = 12 cm.