Pho.rs: Vision

A1 ^0.50 Determine the coefficient $k$. The distance between the thumb and the eye is $l=60$ cm.

A2 ^0.20 Determine the distance $r$ to the car from the example above.

A3 ^0.70 A person observes a tree with a height of $h=3.0$ m at a distance of $d=100$ m. It turns out that the size of the tree's image on the retina is $l=0.6$ mm. Using this data, determine the focal length $F$ of the crystalline lens. The optical system of the eye can be considered to consist of a single thin converging lens (the crystalline lens) and a screen (the retina) on which the image is formed.

A4 ^0.40 Choose which lenses (Figure 2) are suitable for glasses to correct farsightedness. Farsightedness is a condition where distant objects are seen clearly but near objects appear blurred. Lenses are made of glass with a refractive index greater than that of air.

A5 ^1.00 A very nearsighted person's eye lacks accommodation, meaning this person's eye can only clearly see objects at a distance of $x = 25$ cm. Determine the focal length of glasses would be needed so that this person could clearly see very distant objects. Here we neglect the distance between the lens of the eye and the lens of the glasses. What lens shape (Figure 2) would be suitable for such glasses?

A6 ^0.30 The argon-fluorine excimer laser generates ultraviolet radiation with a wavelength of $\lambda=193$ nm. Calculate the energy of one photon of this radiation.

A7 ^0.40 The "evaporation" of microscopic tissue layers using a controlled laser beam occurs due to several processes, one of which is bond cleavage. Compare the obtained laser photon energy with the energies of chemical bonds in corneal biomolecules. Mark the bonds for which the excimer laser photon energy suffices for cleavage.

$E_{\mathrm{(C-C)}} = 348$ kJ/mol
$E_{\mathrm{(C-N)}} = 305$ kJ/mol
$E_{\mathrm{(N-H)}} = 391$ kJ/mol
$E_{\mathrm{(C-H)}} = 413$ kJ/mol
$E_{\mathrm{(C-O)}} = 360$ kJ/mol
$E_{\mathrm{(O-H)}} = 463$ kJ/mol

B1 ^0.70 Calculate the molar mass of the opsin P08100. Round your answer to the nearest whole number. Ignore any post-translational modifications. The molar masses of amino acids are provided in the answer sheet.

B2 ^0.20 The figure shows two absorption spectra (Figure 3). Determine which form of the protein (opsin or rhodopsin) these spectra correspond to.

B3 ^0.50 Determine the concentration of retinaloxime in the solution at the end of the experiment if the optical path was $l=10$ mm.

B4 ^0.50 Determine the extinction coefficient of rhodopsin $\varepsilon_{500}^{Rhodo}$ based on the experimental data.

B5 ^0.40 Determine the number of rhodopsin molecules in the solution if the volume of the solution $V=2$ ml, the optical path $l=10$ mm.

B6 ^0.30 Determine the ratio $r$ of the sensetivities of the long-wavelength $L$ and medium-wavelength $M$ cones to excitation by monochromatic yellow light ($580$ nm).

B7 ^0.80 Determine the intensity ratio $x$ of a mixture of red ($630$ nm) and green ($530$ nm) light so that this light is perceived as yellow from the previous question.

B8 ^1.10 The light now contains a mixture of three colors: red ($650$ nm), green ($547$ nm), and violet ($420$ nm). What intensity ratio ($y$: red/violet, $z$: green/violet) must be taken to produce a color identical to the monochromatic color corresponding to a wavelength of $500$ nm (blue)? Is it possible to obtain the desired monochromatic color by mixing three selected colors?

B9 ^0.50 A father and son have protanopia, but the mother has normal color vision. From whom (mother/father/unable to determine) did the son inherit his protanopia?

B10 ^1.00 A man with deuteranopia and protanopia married a woman with normal vision. They had a son with deuteranopia (without protanopia) and a daughter with protanopia (without deuteranopia). What is the probability of this marriage having a healthy child? What is the probability of having a child with both anomalies?

B11 ^1.10 A man with protanopia and tritanopia married a woman with normal vision. They had a son with tritanopia (without protanopia) and a daughter with protanopia (without tritanopia). What is the probability of having a healthy child from this marriage? What is the probability of having a child with both anomalies?

C1 ^0.70 Specify the maximum absorption spectra of the samples (with an accuracy of $\pm 10$ nm).

C2 ^0.30 Determine which direction (outward or inward) the proton is pumped in this experiment?

C3 ^0.60 Estimate the initial pumping rate $q$. The pumping rate equals to the number of protons pumped per unit of time by microbial rhodopsins through all the cells of this experimental system.

C4 ^0.50 Estimate the surface area of one E. coli cell using electron microscopy image (Figure 9).

C5 ^0.50 Estimate the pumping rate $q_1$ through one molecule of microbial rhodopsin. The cell concentration in the vessel is $n_{cells}=6.4 \cdot 10^9$ ml$^{-1}$. Electron microscopy analysis of the membrane surface revealed that the concentration of microbial rhodopsin molecules on the membrane surface is $\sigma = 5 \cdot 10^3~\mu m^{-2}$.

C6 ^0.90 Based on the results of the experiment, determine $\alpha$. Indicate the units of measurement for $\alpha$.

Vision

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